SOLUTION: I'm not sure if this is the right category but here is my problem: Lupe's mother paid $7.40 to buy juice for the 14 members of Lupe's softball team. If a bottle of orange juice

Algebra ->  Human-and-algebraic-language -> SOLUTION: I'm not sure if this is the right category but here is my problem: Lupe's mother paid $7.40 to buy juice for the 14 members of Lupe's softball team. If a bottle of orange juice       Log On


   

Question 95912: I'm not sure if this is the right category but here is my problem:
Lupe's mother paid $7.40 to buy juice for the 14 members of Lupe's softball team. If a bottle of orange juice costs 55 cents and a bottle of apple juice costs 45 cents, how many of each type did she buy?

I have tried trial and error, and I have gotten the correct answer (3 apple, 11 orange) however, trial and error can take a long time for larger numbers and so I would like to know what the algebraic equation is, preferably using 1 variable. thank you for your time
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=14 OR X=14-Y
55X+45Y=740 NOW REPLACE X WITH(14-Y) & SOLVE FOR Y
55(14-Y)+45Y=740
770-55Y+45Y=740
-10Y=740-770
-10Y=-30
Y=-30/-10
Y=3 AMOUNT OF APPLE JUICE BOUGHT
X=14-3=11 ORANGE JUICE BOUGHT.
PROOF
55*11+45*3=740
605+135=740
740=740