Problem Solving

BTGmoderatorLU wrote:Source: Veritas Prep

Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?

A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7

The OA is C

We see that we need 25 ounces of salt. We can go through the choices:

A) 6:4

6x + 4x = 50

10x = 50

x = 5

So we have 6(5) = 30 ounces of A and 4(5) = 20 ounces of B. Does this produce 25 ounces of salt?

30 x 0.2 + 20 x 0.8 = 6 + 16 = 22 → No

B) 6:14

6x + 14x = 50

20x = 50

x = 2.5

So we have 6(2.5) = 15 ounces of A and 14(2.5) = 35 ounces of B. Does this produce 25 ounces of salt?

15 x 0.2 + 35 x 0.8 = 3 + 28 = 31 → No

C) 4:4

This means we have 25 ounces of A and 25 ounces of B. Does this produce 25 ounces of salt?

25 x 0.2 + 25 x 0.8 = 5 + 20 = 25 → Yes!

Alternate Solution:

Let A be the amount of Solution A and B be the amount of Solution B that produces a 50% salt solution when mixed. Since we want 50 ounces of 50% salt solution, there must be 50 x 0.5 = 25 ounces of salt in our solution.

We have the following:

A + B = 50

0.2A + 0.8B = 25

Let's rewrite these two equations:

2A + 2B = 100

2A + 8B = 250

Let's subtract the first equation from the second:

6B = 150

B = 25

Since A + B = 50, A = 25 also. Since there are A = 25 ounces of solution A and B = 25 ounces of solution B in our mixture, we need to mix A and B in the ratio of 1:1; or equivalently, 4:4.

Answer: C