Question

1. (4 points) Betsy wants to make a solution of sulfuric acid that is 47% acid. Currently, her lab has a

21% solution and a 75% solution. How much of each would be required to make 3 liters of 47% solution?
Answer with the exact solution and the approximation.

Answer 1

x = amount (in L) of 21% solution

y = amount (L) of 75% solution

Betsy wants to end up with 3 L of solution:

x + y = 3

And she wants the final mixture to consist of 47% acid:

0.21x + 0.75y = 0.47(x + y) = 1.41

y = 3 - x

0.21x + 0.75(3 - x) = 1.41

0.21x + 2.25 - 0.75x = 1.41

0.84 = 0.54x

x = 1.555...

==> y = 1.444...

To get exact values, notice that

10x = 15.555... ==> 10x - x = 9x = 14 ==> x = 14/9

10y = 14.444... ==> 9y = 13 ==> y = 13/9