SOLUTION: At the fruit market, a box of 16 peaches costs $2.01 more than a bag of 12 apples. Bobby bought 2 boxes of peaches and 5 bags of apples. He paid $46.11, which included 6% sales tax

Algebra ->  Equations -> SOLUTION: At the fruit market, a box of 16 peaches costs $2.01 more than a bag of 12 apples. Bobby bought 2 boxes of peaches and 5 bags of apples. He paid $46.11, which included 6% sales tax      Log On


   



Question 438404: At the fruit market, a box of 16 peaches costs $2.01 more than a bag of 12 apples. Bobby bought 2 boxes of peaches and 5 bags of apples. He paid $46.11, which included 6% sales tax. What is the price of each box of 16 peaches and what is the price of each bag of 12 apples?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the price of a box of 16 peaches
Let b = the price of a bag of 12 apples
Let c = the price of 2 boxes of peaches and 5 bags of apples
given:
(1) +a+=+b+%2B+201+ (in cents)
(2) +2a+%2B+5b+=+c+ (in cents)
+c+%2B+.06c+=+4611+ (in cents)
+c+=+4611%2F1.06+
+c+=+4350+ ( in cents)
-----------------------
(1) +a+-+b+=+201+
(2) +2a+%2B+5b+=+4350+
Multiply both sides of (1) by 5 and add (1) and (2)
(1) +5a+-+5b+=+1005+
(2) +2a+%2B+5b+=+4350+
+7a+=+5355+
+a+=+765+
and, since
(1) +a+-+b+=+201+
+765+-+b+=+201+
+b+=+765+-+201+
+b+=+564+
Each box of 16 peaches costs $7.65
Each bag of 12 apples costs $5.64
check:
(2) +2a+%2B+5b+=+c+
(2) +2%2A765+%2B+5%2A564+=+4350+
+1530+%2B+2820+=+4350+
+4350+=+4350+
OK