Please help me im in danger of staying back :(

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 20% salt and Solution B is 45% salt. She wants to obtain 40  ounces of a mixture that is 35%

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

Solution A

Solution B

Answer 1

We will solve this problem via a system of equations. First, we start by selecting the variables we will work with, identifying what they represent. Since the unknowns are the number of ounces of each solution, let's let A = the number of ounces for solution A, and let's let B = the number of ounces for solution B.

The first equation we will write will deal simply with the total ounces involved. Since the final mixture is a total of 40 ounces and those 40 ounces are made up of amounts from both solutions, the equation is A + B = 40.

The second equation will deal only with the amount of salt in each individual solution and in the final mix. Since solution A is 20% salt, the amount of salt in A can be represented as 0.20A. Since B is 45% salt, the amount of salt in B can be represented as 0.45B. For the final mixture to be 35% salt, we represent this as 0.35(40) ** We multiply the percentage of salt, 35%, by the total ounces in the mixture, which is 40 oz. So the second equation becomes 0.20A + 0.45B = .35(40).

Since the first equation we wrote is an easy one in which to isolate one of the variables, let's take the first equation, isolate A, and the equation becomes A = 40 - B. Now we substitute the expression "40 - B" into our second equation for A, and the second equation becomes 0.20( 40 - B ) + 0.45B = 14. Eliminating the parentheses and combining like terms, we get 0.25B = 6. Dividing both sides by 0.25, we get B = 24. Substituting this value into the first equation, we get A = 16. Checking both values in both equations confirms that we have the correct amounts, so we need 16 oz. of solution A and 24 oz of solution B.