Question

A cleaning solution is made from vinegar, lemon juice, and water. The table below shows the part of the total solution that is in each element.

Solution Components

Solution A
Solution B
Solution C
Vinegar
0.1
0.2
0.4
Lemon Juice
0.15
0.2
0.1
Water
0.75
0.6
0.5

Mr. Allen needs 100 mL of a solution that is 30% vinegar, 15% lemon juice, and 55% water. How much of solution A will Mr. Allen need to make his cleaning solution?
0 mL
10 mL
30 mL
50 mL

Answer 1

Let x,y,z be mL of solutions A, B, C. Then
x + y + z = 100
0.1x + 0.2y + 0.4z = 30
0.15x + 0.2y + 0.1z = 15

From the second and third equations you get z = x + y. Substituting into x + y + z = 100 gives 2(x + y) = 100, so x + y = 50 and z = 50. Using 0.1x + 0.2y + 0.4(50) = 30 yields x + 2y = 100, combined with x + y = 50 gives y = 50 and x = 0.

So Mr. Allen needs 0 mL of solution A.