Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is

40
%

salt and Solution B is
65
%

salt. She wants to obtain
40

ounces of a mixture that is
60
%

salt. How many ounces of each solution should she use?

Answer 1

We need 8 ounces of solution A and 32 ounces of solution B.

Explanation:

We are given that a scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt.

She knows that Solution A is 40% salt and Solution B is 65% salt.

• First condition states that she wants to obtain 40 ounces of a mixture that is 60 % salt, that means;

A + B = 40

B = 40 - A ------------ [Equation 1]

• Second condition states that Solution A is 40% salt and Solution B is 65% salt, that means;

`0.4 \text{A}+0.65 \text{B}=0.60 * 40`

`0.4 \text{A}+0.65 \text{B}=24`

`0.4 \text{A}+0.65 (40- \text{A})=24` {from equation 1}

`0.4 \text{A}+26- \text{0.65A}=24`

`\text{0.65A} - 0.4 \text{A}=26-24`

`\text{0.25A} =2`

A =
`(2)/(0.25)` = 8 ounces

Now, putting value of A in equation 1, we get;

B = 40 - A

B = 40 - 8 = 32 ounces

Hence, we need 8 ounces of solution A and 32 ounces of solution B.