A chemist combines a 60% acid solution with a 90% acid solution to make a final 80% solution that contains 18 ounces. how many ounces of each solution does she

Question

need help with this problem

Answer 1

I believe this might be the way to solve it.

 

Let x be the number of ounces of the 60% solution needed, and y be the number of ounces of the 80% solution needed. Then we have

 

x + y = 18

=> y = 18 - x

 

Since we have 18 ounces of an 80% solution we have a total number of ounces of acid of

 

0.6*x + 0.9*y = 0.8*18 = 14.4

 

We substitute in our previous solution for y to get the equation

 

0.6*x + 0.9*(18-x) = 14.4

 

And then we solve for x.

 

0.6*x + 16.2 - 0.9*x = 14.4

=> 16.2 - 0.3*x = 14.4

=> -0.3*x = -1.8

=> x = 6

 

Then we can solve for y.

 

y = 18 - x

   = 18 - 6 = 12

 

So we need 6 ounces of the 60% solution and 12 of the 90% solution.