SOLUTION: How many cups of grapefruit juice must be added to 40 cups of punch tht is 5% grapefruit juice to obtain a punch tht is 10% grapefruit juice?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: How many cups of grapefruit juice must be added to 40 cups of punch tht is 5% grapefruit juice to obtain a punch tht is 10% grapefruit juice?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 882537: How many cups of grapefruit juice must be added to 40 cups of punch tht is 5% grapefruit juice to obtain a punch tht is 10% grapefruit juice?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
                                        | percentage |     cups of
                                        | expressed  |  grapefruit juice
                       | cups of liquid | as decimal | contained in liquid
-----------------------|----------------|------------|--------------------
  5% grapefruit juice  |      40        |    .05     |    .05(40) = 2    
100% grapefruit juice  |       x        |   1.00     |      1.00x = x
-----------------------|----------------|------------|-------------------- 
     punch mixture     |    40+x        |    .10     |  .10(40+x) = 4+.10x

Equation comes from right-most column:

                                 2 + x = 4+.10x
                              20 + 10x = 40 + x
                                    9x = 20
                                     x = 20%2F9
                                     x = 2%262%2F9 cups

Edwin