SOLUTION: This was a problem on my daughter's test that she got wrong and, for some reason, I keep getting it wrong as well. Here it is exactly as it was given to us. The 20 per pound sounde

Question 806787: This was a problem on my daughter's test that she got wrong and, for some reason, I keep getting it wrong as well. Here it is exactly as it was given to us. The 20 per pound sounded weird to me but I'll let you all look at it. I tried to solve it using 4.2x + 3.6(20-x) = 20(4) and I did not get what the teacher got. She used a different system to solve.
A supermarket sells a mixture of roasted nuts and raisins. Roasted nuts sell for $3.60 per pound, and raisins sell for $4.20 per pound. The supermarket wants to make a 20 per pound mixture that sells for $4.00 per pound. Write a system of equations and determine how many pounds of roasted nuts and raisins the supermarket should mix.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your equation is fundamentally correct, and given correct arithmetic you should have arrived at the correct numerical answer of 13 and 1/3 pounds of raisins and 6 and 2/3 pounds of nuts.

Where you may be running afoul of the teacher's system is that you did not precisely follow the instructions in the problem. You wrote a single equation and the problem asks for a system of equations. In this sort of scenario, you can write two equations in two variables. Here, we need a quantity equation and a value equation:

First, declare your variables. Let

represent the number of pounds of raisins, and let

represent the number of pounds of nuts.

Quantity equation:

Value equation:

This particular problem is going to degenerate into the same thing you started with when you solve the quantity equation for

and then solve the system using the substitution method. But I suspect the teacher is in the process of introducing the idea of systems of equations, and the lesson here is for the student to understand the structure of linear systems and the process of solving them -- whether or not you can figure out how many pounds of raisins you need for the 20 lb mixture is immaterial.

Hope that helps.

John

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