SRL Archive - Mathematics

Everyday my school hands out a math problem for the students to solve. The one with the highest score till Christmas wins something:spot:
Sadly I didn't hear about this before the 12th, so I hope my fellow students suck at math so I might have a chance.
New edit everyday, and thanks in advance!

12th
When the camel is thirsty, she consists of 84% water.
After she drinks, she weights 800kg, and the water percentage rises up to 85%.
How much does she weight when she's thirsty?
Answer: 750kg
First answered by Solar Virus

13th
Which number comes next?
4, 9, 17, 29, 46, 69…
Answer: 99
First answered by DeiJaiVui

14th
The Adams family have eaten pancakes. There is 1 liter of the liquid pancake mix stuff left. The mother is going to freeze it. The mother knows it takes exactly 5 scoops to fill the box she is putting it in. But she can't find the scoop, so she uses a smaller scoop. This scoop is half the size of the first one that she couldn't find. Both scoops are half-sphere shaped.
How many scoops would the mother need to fill the box?
Answer: 40
First answered by Enslaved

15th
Normally it would take 15 minutes to fill the bathtub for the Adams family. But this one time they forgot to seal the drain thing. So it took an hour to fill the bathtub now this time.
So if the bathtub is full, how long would it take to empty the whole bathtub through the drain?
Answer: 20 minutes
First answered by masterBB

16th
We fill half the cone's volume with water, which is upsidedown where height = 1.
What is the height of the water?
Answer: The height of the water level is variable to the radius of the cone.
First answered by Enslaved

17th I didn't understand this one, so I'll just translate what it says.
We're going to split a circle in as many pieces possible, with 7 straight lines.
How many pieces can you get?
Answer: 29
First answered by Turpinator

18th
At the local market garden, there's both male and female employees. 1/3 of the employees brings a child each to work everyday they're going to plant trees. Every male employee plants 13 trees, every female plants 10 trees and every child plants 6 trees. A total of 159 planted that day.

How many female employees are there?

The questions grammar is a tad off, i cant be bothered to actually do it, but damn that camel being made from 84% water is interesting

750 kg.

The weight of the non-water mass is 120 kg. (800 x .15)
So, since the non water weight doesn't change (i assume) use that to find the total weight by dividing the 120 kg by the percentage of mass it takes up (120 / .16)

From: Solar Virus
750 kg.

The weight of the non-water mass is 120 kg. (800 x .15)
So, since the non water weight doesn't change (i assume) use that to find the total weight by dividing the 120 kg by the percentage of mass it takes up (120 / .16)

Why do you multiply 800 with .15? Where do you get from 0.15?

From: bi a op
Why do you multiply 800 with .15? Where do you get from 0.15?

The camels weight after drinking is 800kg, which is made up of 85% water and (100-85)%=15% of the camels own weight.

I know this question has already been answered, but here is how I ended up doing it.

From: bi a op

When the camel is thirsty, she consists of 84% water.
After she drinks, she weights 800kg, and the water percentage rises up to 85%.
How much does she weight when she's thirsty?

The answer to this question is…

Weight of camel after drink = 800kg with 85% of that weight being water
Weight of camel before drink = Xkg with 84% of that weight being water

Assuming all weight gained while drinking came from the water intake, no water was lost through sweat, urination etc… and its mass that isn't water remained unchanged…

…we first need to work out the mass that isn't water by finding the percentage that isn't water and multiplying it by the total mass. (using the values from after drinking)

800kg x (100%-85%) = 800kg x 0.15 = 120kg

The percentage of mass that isn't water before drinking is (100%-84%) 16%.
Therefore, since I'm assuming 120kg is constant,
16% = 120kg in this case.

Using that information we can work out that 100% = 750kg

The question is wrong. This is not math, this is stupid. I can't solve it.

edit:

Changing the question and assuming this:

Weight of camel after drink = 800kg with 85% of that weight being water
Weight of camel before drink = Xkg with 84% of that weight being water

the weight will be 792 kg.

why?

because:
amount of weight * water percentage = water weight
800 kg * 85 % = 680 kg of water

85% water = 680 kg
1% water = 8 kg

the camel weights 1% less so:
800kg - 8 kg = 792kg

From: masterBB
The question is wrong. This is not math, this is stupid. I can't solve it.

edit:

Changing the question and assuming this:



the weight will be 792 kg.

why?

because:
amount of weight * water percentage = water weight
800 kg * 85 % = 680 kg of water

85% water = 680 kg
1% water = 8 kg

the camel weights 1% less so:
800kg - 8 kg = 792kg

Correct.

From: masterBB
The question is wrong. This is not math, this is stupid. I can't solve it.

edit:

Changing the question and assuming this:



the weight will be 792 kg.

why?

because:
amount of weight * water percentage = water weight
800 kg * 85 % = 680 kg of water

85% water = 680 kg
1% water = 8 kg

the camel weights 1% less so:
800kg - 8 kg = 792kg

That's what I got too.

From: Aqua3
Correct.

Incorrect, because the % of water is not the same when he is thirsty and when he is satisfied.

The wight without water of the camel is a constant. This wight will not change if his is thirsty or not, while the weight of the water will so its a variable.

In conclusion you cant take water as a constant of 85% but you can take camel dry weght as a constant of 15% because this will never change.

so 15% of 800kg = 120kg
this 120kg will never change because is the camel dry weight (a constant)
So independly if your camel has 85 or 84 % of water this will be 15 %.
well i think so hahaha

^^^E: Referring to previously made post about 792kg being the answer.

No this is not correct.
This would mean that 1% of 800kg is the same as 1% of weight before, which can not be true. Also it means that the camel consists of 100% water. A % change of water content does not mean the same % change of total mass. These two things might be hard to understand, but there is no need to rephrase this question and your answer is not correct.

You might find a drastic weight change of 50kg (from 750-800) quite hard to believe, but after doing some research like I did you will find that camels can drink A LOT of water in one go in order to survive in the desert for weeks without water!

http://www.loc.gov/rr/scitech/mysteries/camel.html
'They drink large amounts of water - up to 20 gallons at a time. This water is stored in the animal's bloodstream.'
20 gallons converts to 91 litres to the nearest litre!

Of course litres and kg are not one and the same thing, but 1 litre of water is in fact roughly 1 kg!

http://en.wikipedia.org/wiki/Litre
'From 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at 4 °C and 760 millimetres of mercury pressure.'

So yes, a change of 50kg is feasible. There is no need to change the question around as apart from a few assumptions…
1.Non-H2O mass of camel is constant throughout
2.No mass is lost through excretion
…and a few others I can't think of right now the question is perfectly fine!
As crazy as this might seem - the camel gained 50kg in weight.

750 is the correct solution.

Water percentage = weight of water / total weight * 100

85% = weight of water / 800kg * 100
weight of water = 680kg
weight of non-water (800 - 680)= 120kg

Let x be equal to the camel's total weight at 84% water.
84 = (x - 120) / x * 100
x = 750kg

check:
Water percentage = weight of water / total weight * 100
84 = (750 - 120) / 750 * 100
84=84

From: Runehack123
^^^E: Referring to previously made post about 792kg being the answer.

No this is not correct.
This would mean that 1% of 800kg is the same as 1% of weight before, which can not be true. Also it means that the camel consists of 100% water. A % change of water content does not mean the same % change of total mass. These two things might be hard to understand, but there is no need to rephrase this question and your answer is not correct.

Nowhere there is stated that percentage is a percentage of mass. Or a percentage of volume. Or maybe even a percentage of smell. Who knows? To make it easy I assumed they meant percentage of mass.

The mistake I made was taken the 84% of the 800kg, which it was not. Obviously your answer is right. 750 kg

From: Runehack123
^^^E: Referring to previously made post about 792kg being the answer.

No this is not correct.
This would mean that 1% of 800kg is the same as 1% of weight before, which can not be true. Also it means that the camel consists of 100% water. A % change of water content does not mean the same % change of total mass. These two things might be hard to understand, but there is no need to rephrase this question and your answer is not correct.

You might find a drastic weight change of 50kg (from 750-800) quite hard to believe, but after doing some research like I did you will find that camels can drink A LOT of water in one go in order to survive in the desert for weeks without water!

http://www.loc.gov/rr/scitech/mysteries/camel.html
'They drink large amounts of water - up to 20 gallons at a time. This water is stored in the animal's bloodstream.'
20 gallons converts to 91 litres to the nearest litre!

Of course litres and kg are not one and the same thing, but 1 litre of water is in fact roughly 1 kg!

http://en.wikipedia.org/wiki/Litre
'From 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at 4 °C and 760 millimetres of mercury pressure.'

So yes, a change of 50kg is feasible. There is no need to change the question around as apart from a few assumptions…
1.Non-H2O mass of camel is constant throughout
2.No mass is lost through excretion
…and a few others I can't think of right now the question is perfectly fine!
As crazy as this might seem - the camel gained 50kg in weight.

Yes, the water isn't a constant variable, however the non-water matter is. By the way, a problem doesn't have to make sense logically for an answer to be correct (ex. The camel jumped to 98% water weight after drinking), I've seen some pretty bizarre problems. ;)

From: masterBB
Nowhere there is stated that percentage is a percentage of mass. Or a percentage of volume. Or maybe even a percentage of smell. Who knows? To make it easy I assumed they meant percentage of mass.

The mistake I made was taken the 84% of the 800kg, which it was not. Obviously your answer is right. 750 kg

Actually, in the question it states that the % is a percentage of water.
'When the camel is thirsty, she consists of 84% water.'
On a chemical level, % of substance means % of substance in moles compared to a total number of moles within a system. Therefore, comparing a mass to a total mass within a system.

Please post answer when you find it out in class.
Been 30 years since i've done math but it seams to me you guys are over analysing this.
we know camel weights 800kg @ 85% water. Divide 800 by 85 would give you what 1% would be which is 9.4117647058823529411764705882353 or rounded down which would be 9.41
800 - 9.41 = 790.59kg
or rounded up to 791kg
Again been along time for math problems for me so please post school answer when found out.

From: wyo64
Please post answer when you find it out in class.
Been 30 years since i've done math but it seams to me you guys are over analysing this.
we know camel weights 800kg @ 85% water. Divide 800 by 85 would give you what 1% would be which is 9.4117647058823529411764705882353 or rounded down which would be 9.41
800 - 9.41 = 790.59kg
or rounded up to 791kg
Again been along time for math problems for me so please post school answer when found out.

We've already all established that the correct answer is 750kg and it has been discussed in detail by several people now.

School answer has already been posted several times now! :)

https://www.dropbox.com/s/kfxr7y061gjadcl/2012-12-12_17-30-42_817.jpg

Thanks for your answers! I answered 750kg, let's hope it's correct (ofc it is).
New one tomorrow. I'll edit the first post.

From: bi a op
Thanks for your answers! I answered 750kg, let's hope it's correct (ofc it is).
New one tomorrow. I'll edit the first post.

Oh god, I hope it makes more sense.

From: Runehack123
Actually, in the question it states that the % is a percentage of water.
'When the camel is thirsty, she consists of 84% water.'
On a chemical level, % of substance means % of substance in moles compared to a total number of moles within a system. Therefore, comparing a mass to a total mass within a system.

In moles it wouldn't make sense without a very big and complete study of the kind of moles in a camel. Which of course isn't required. Because if the camel exist out of 85% water and 15% lead, the weight of the lead would be a lot higher compared to when it would have existed out of 15% solid helium.

From: masterBB
In moles it wouldn't make sense without a very big and complete study of the kind of moles in a camel. Which of course isn't required. Because if the camel exist out of 85% water and 15% lead, the weight of the lead would be a lot higher compared to when it would have existed out of 15% solid helium.

Yes, that was wrong what I said there sorry.
It's actually the % mass as you convert the moles into mass first then calculate the percentage.
That should make more sense! :D

From: Runehack123
Yes, that was wrong what I said there sorry.
It's actually the % mass as you convert the moles into mass first then calculate the percentage.
That should make more sense! :D

Moles are not needed period, these are logic question that involve basic algebra :P

New problem!:spot:

5 8 12 17 23

each interval add the next one

so the next number would be +30

69+30 = 99

From: DeiJaiVui
5 8 12 17 23

each interval add the next one

so the next number would be +30

69+30 = 99

I don't understand, can you explain it differently? :P

From: bi a op
I don't understand, can you explain it differently? :P

here you go buddy.

May I ask you what year you are in or grade for the Americans?

From: DeiJaiVui
here you go buddy.

http://i48.tinypic.com/21dipg0.png

I see! Thanks :D

From: Mr[S]
May I ask you what year you are in or grade for the Americans?

If you're asking me. It would be Senior High, 12th grade. I'm 17.

Let's hope tomorrows problem will be more challenging.

From: bi a op
I see! Thanks :D



If you're asking me. It would be Senior High, 12th grade. I'm 17.

Let's hope tomorrows problem will be more challenging.

Lol.. I'm in Grade 7, Australia. xD

This is already answered and such, but in hopes of not having the confusion we had with yesterdays i will attempt to explain it. Basically… You look at the difference in each term and their differences until you come to a constant number.

There's a new problem.

10 I assume.

The Adams family have eaten pancakes. There is 1 liter of the liquid pancake mix stuff left. The mother is going to freeze it. The mother knows it takes exactly 5 scoops to fill the box she is putting it in. But she can't find the scoop, so she uses a smaller scoop. This scoop is half the size of the first one that she couldn't find. Both scoops are half-sphere shaped.
How many scoops would the mother need to fill the box?

Yeah, trick question though? I'd assume it would be 10 too..

lol at the answers

Assuming that the Scoop is a perfect half sphere

For enslaved.

damn, I am never first. At least I am most readable :P

edit:

Also made a mistake swapping the 4 and 3, oh well. Answer is correct.

The main part its (r/2)^3 which makes the difference to be 8x r' the front part doesn't matter as it is constant in both

@ masterbb, what did you type that up in? Mathematica?

From: Enslaved
@ masterbb, what did you type that up in? Mathematica?

word(file attached)

Press left alt and (+=) to insert formula.

From: Enslaved
lol at the answers

Assuming that the Scoop is a perfect half sphere
http://i.imgur.com/ywWN1.png

Wow, that's pretty neat. I was 1 hour too late to answer that days question so I emailed the admin with my answer. He accepted the answer because it was correct. This is genious :D

Also, there's a new problem.

20 minutes

see: http://ancientbb.com/Water%20in%20the%20bathtub.pdf

New problem. 15th can still be answered.

was my previous answer not correct?

From: bi a op
New problem. 15th can still be answered.

You meant qns 16?
I get the same ans as masterBB for 15, though a much shorter way ;)
fill rate = 1 bathtub per 15 min (1/15)
fill rate - drain rate = 1 bathtub per 60 min (1/60)
drain rate = 1/15 - 1/60 = 1/20 (1 tub / 20min)
time needed to drain 1 bathtub = 20min


For qns 16, what 'cone' are you referring to? The bathtub is a cone? :p

From: riwu
You meant qns 16?
I get the same ans as masterBB for 15, though a much shorter way ;)
fill rate = 1 bathtub per 15 min (1/15)
fill rate - drain rate = 1 bathtub per 60 min (1/60)
drain rate = 1/15 - 1/60 = 1/20 (1 tub / 20min)
time needed to drain 1 bathtub = 20min


For qns 16, what 'cone' are you referring to? The bathtub is a cone? :p

I do it like in one step in my head. But I try to explain it as much detail as possible. Most steps dont do anything.

the height of the water level is variable to the radius of the cone

From: bi a op

16th
We fill half the cone's volume with water, which is upsidedown where height = 1.
What is the height of the water?

Im confused on this one… What is the height of the water if the cone is turned the other way? ( like this – /\ ) or is it meant to say what is the height of the cone?

Either way, height of the water if the cone is flipped around = sqrt2 -1 ~ .41 units
Height of the cone = sqrt2 ~ 1.41 units

#10

From: Enslaved
lol at the answers

Assuming that the Scoop is a perfect half sphere

From: Turpinator
Im confused on this one… What is the height of the water if the cone is turned the other way? ( like this – /\ ) or is it meant to say what is the height of the cone?

Either way, height of the water if the cone is flipped around = sqrt2 -1 ~ .41 units
Height of the cone = sqrt2 ~ 1.41 units

From: Enslaved
the height of the water level is variable to the radius of the cone

You're all correct, look at answer D :duh:

New problem for 17th!

From: bi a op
17th I didn't understand this one, so I'll just translate what it says. Answers ABCD are included
We're going to split a circle in as many pieces possible, with 7 straight lines.
How many pieces can you get?
14, 29, 35, 49, 128

29.
Basically each time you add another line, you add the previous amount of lines placed, but we get to start at 1.
0 lines = 1 section
1 line = 0 lines + 1 section = 2 sections
2 lines = 1 line + 3 sections = 4 sections… etc
3 lines = 4 +3 = 7 sections
4 lines = 7 + 4 = 11 sections
5 lines = 11 + 5 = 16 sections
6 lines = 16 + 6 = 22 sections
7 lines = 22 + 7 = 29 sections

The pattern for this one also matches how you would do the 13th. 1, 2, 4, 7, 11, 16, 22, 29, 37…
where f(x) is the number of sections with x lines, f(x) = (x*(x+1) +2)/2

agreed with turpinator 29

Agreed

New problem for the 18th!

#18:
7 females.

  for f:=0 to 100 do
    for m:=0 to 100 do
      if (f + m) MOD 3 = 0 then
        if (13 * m + 10 * f + (1.0 / 3) * (m + f) * 6) = 159 then
          writeln(Point(f, m)); 

(7, 5)

Awkward moment when he only had 7 math problems for homework.
You have all been played. :)

Luls. he wrote a script to 'bruteforce' the answer.
Very nice though. Much easier than guess and check by hand eh?

From: Turpinator
Luls. he wrote a script to 'bruteforce' the answer.
Very nice though. Much easier than guess and check by hand eh?

Well there's no way to solve it algebraically since there's 3 unknowns but only 2 equations, so will have to do trial and error with f + m being multiples of 3 ;)
The question is unconventional though, usually it should give us 3 equations for 3 unknowns then we can solve it with matrices (system of linear equations).

f * 10 + c * 6 + m * 13 = 159

(m + f) / 3 = c



f * 10 + ((m + f) / 3) * 6 + m * 13 = 159


10f + 6((m + f) / 3) + 13m = 159


10f + 2(m + f) + 13m = 159

10f + 2m + 2f + 13m = 159


12f + 15m = 159


f = 159 - 15m / 12


Since there can only be integers of f…


m = 1,5,9


f = 12,7,2


*gasps* wow omg


I believe the question posted isn't complete unless your teacher wants you to randomly pick 1..

It seems the solution is right…