I have a math question... Is my answer right?

Question

we have a packet of math to do before school starts... No big deal. 85 questions. But question 85 drove me MAD. I think I figured out aAN answer... but I need to know if it's right or not. And if it is... How the heck I got it.

From the sheet:

85. How many ounces of a 25% acid solution should be mixed with a 50% acid solution to produce 100 ounces of a 40% acid solution?

So I though I'd make

.25x + .5y = .4

x + y = 100

But it drove me insane. I tries a million different variations, to no avail. then, I have no clue why I tried this, I came up with

.25x + .5y = 40

x + y = 100

And I came up with x equilling 20 (oz.) and y equiling 80 (oz.) I plugged them into the equation, and they actually fit. But I still think I'm way off. Can someone show me how to solve this type of problem, and tell me if I'm wrong or not? And if I am wrong, what I did wrong?

Answer 1

0.25x + 0.5y = 40

x + y = 100

Your second set of equations is correct. The first set was wrong because of the error in 0.25x+0.5y = 0.4. I know you'll be mad about this but you forgot to multiply the 0.4 by the volume to which it applies, in this case 100 oz, and of course, 0.4 x 100 = 40  

Answer 2

First, set up the correct equations:

0.25x +0.5 y= 0.4 *100  the total acid content

x + y = 100  

Which were your second set of equations.

But, Your did not find the correct answers.

To solve them, try to eliminate one variable form the equations:

such as; multiple the first by 4 => x +2y=160

and then subtract the second equation => y=60,

then  x=100 -y =40

answer: x=40, y=60.

substitute them them back to equation to check if they are correct.

There is another way to do it without equations.

We have 25% and 50% solutions.

If we mixed them half and half, then we get 37.5%.

40% is 15% from 25% and 10% from 50%.

which is 2 to 3 ratio. So, just reverse the ratio,

use 2 parts of 25%, and 3 parts of 50% solutions.

So, cut 100 oz into 5 parts.

We will need 40 oz of 25% and 60 oz of 50% solutions.