SOLUTION: Julia's punch recipe calls for a 3:1 ration of Puerto rican rum (40% alcohol) to Jamaican rum (50% alcohol), mixed with Hawaiian punch. From past experience, Julia knows that if he

Question 1058836: Julia's punch recipe calls for a 3:1 ration of Puerto rican rum (40% alcohol) to Jamaican rum (50% alcohol), mixed with Hawaiian punch. From past experience, Julia knows that if her brother john drinks more than 2 ounces of alcohol, he will take too much time saying grace. Yet, brother John always has an 8-ounce glass of rum punch. If Julia uses 96 ounces of Hawaiian punch, what is the maximum number of ounces of Jamaican rum she can use to keep brother John from taking too much time to say grace (round down to the nearest whole number).
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

For an 8-oz glass of rum punch to contain 2 ounces of alcohol, it
must be 2/8 or 1/4 or 25% alcohol.  So the rum punch she fixes must 
be 25% alcohol to have the maximum strength.      

Let x = the number of ounces of Jamaican rum.
Then since the ratio of Puerto Rican to Jamaican is 3:1
there will be 3x ounces of Puerto Rican rum.  So
make this table:

                  |ounces|  percent   |ounces of
                  |  of  |  alcohol   | alcohol
                  |liquid| as decimal |contained 
---------------------------------------------------
Puerto Rican rum  |  3x  |  0.40      | 0.40(3x)         
Jamaican rum      |   x  |  0.50      | 0.50(x)    
Hawaiian punch    |  96  |  0.00      | 0.00(96)
---------------------------------------------------       
rum punch         |4x+96 |  0.25      | 0.25(4x+96)

The equation is found by adding the ounces of alcohol 
contained in the three liquids and setting it equal to 
the ounces of alcohol to be contained in the rum punch.

                0.40(3x) + 0.50(x) + 0.00(96) = 0.25(4x+96)

Simplify and solve that for x and round down to the nearest
integer to get your answer.

Edwin

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