math word problem

Question

jessica asked you to make 16L of fruit punch that contains 25% fruit juice by mixing together some amount of brand A fruit punch and some amount of brand B. Brand A contains 10% fruit juice Brand B contains 34% fruit juice. How much of eachdo you use?

Answer 1

To solve this problem, we need to generate a system of equations. We can use the variable A to represent Brand A and the variable B to represent Brand B. The problem tells us that a total of 16L of fruit punch must be made. This translates to A+B=16. That is our first equation. Next, the problem tells us that Brand A contains 10% fruit juice, while Brand B contains 34% fruit juice. When added together, the amount of Brand A and the amount of Brand B must equal 16L of fruit punch with 25% fruit juice. When translated into an equation, we find that 10%A+34%B=25%(16). If we convert these numbers to decimals, the equation becomes 0.10A+0.34B=0.25(16). To make this easier to work with, we can multiply this entire equation by 100, which will get rid of the decimals. The equation becomes 10A+34B=400. You should notice that when you multiply the decimals by 100, you end up with the same equation we found with the percentages. So now we have our two equations. 

 

10A+34B=400

(A+B = 16)*10

 

We can multiply the bottom equation by 10, so that we can eliminate the A variable from our system.

 

     10A+34B=400

-    10A+10B=160

     

             24B=240

                B=10

 

To determine how many liters (L) of Brand A are needed, we can plug B=10 into the equation A+B=16. 

A+10=16

A=6

 

Thus, you would need 6 liters of Brand A and 10 liters of Brand B.