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# Science and Salt

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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 80% salt . She wants to obtain 110 ounces of a mixture that is 60% salt. How many ounces of each solution should she use?

Jun 28, 2023

#1
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Let x be the number of ounces of Solution A and y be the number of ounces of Solution B. We know that x + y = 110 ounces. The total amount of salt in the resulting solution must be 60% of the final solution, so 0.55x + 0.8y = 0.6(x+y) = 0.6 * 110 = 66 ounces. Solving the system of equations x + y = 110 and 0.55x + 0.8y = 66, we get x = 40 and y = 70. Therefore, the scientist should use 40 ounces of Solution A and 70 ounces of Solution B.

Jun 28, 2023
#2
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Let the amount of solution A needed==A

Then, the amount of solution B needed==110  -  A

0.55A  +  0.80[110  -  A] ==0.60 * 110, solve for A

A==88 ounces of solution A will be needed

110  -  88 ==22 ounces of solution B will be needed.

Jun 28, 2023