SRL Archive - Mathematics

I havn't used this site in a long time but I remember this math page being useful for basic math problems which I found frustrating. This problem is insanly stupid but I need it to write a program in order to maximise the yield. It's kinda like balancing heat and pressure in the production of ammonia which I forgot how to do because of bad memory + bad chem student.

So just to make things easier I will simplify the question, and use buttons to represent the variables.

So lets say 1 package(1) contains 75 blue buttons and 100 red buttons and another package(2) contains 125 blue buttons and 50 red buttons.

Now the ratio of of blue:red for the packages are:

3:4 - (1)
5:2 - (2)

Now I want to figure out some method for balancing the ratios of the packages so the ratio of blue buttons to red buttons is 1:1.

So inception with ratios

Total amount of buttons is 175.
R+B = 175 so R = 175 - B
you want R = B
So 175 - B = B

Leads to 2b = 175 -> b = 175/2 = 87,5 blue buttons or red buttons.
Unless you're looking for something else?

edit: read the question again this doesnt make sense. might look at it later, sleep deprivation for the lose.

blue 75+125=200/2=100
red 100+50=150/2=75

So you can't really have 1:1 ratio unless you can drop few blues.

Sorry, I worded it badly. If you have 3 of package (1) and 2 of package (2) you get a combined ratio of 19:16

It is defiantly possible.

EDIT: Solved, just some really easy algebra…

3x + 5y = 4x +2y

3y = x

3 = x/y

I feel like a dumbass, I wish I was sober when I was trying to figure this out…