SOLUTION: the price of a pound of cherries is $0.30 more than five times the price of a pound of apples. The price of a pound of bananas is $0.10 less than double the price of apples. Joe bo

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: the price of a pound of cherries is $0.30 more than five times the price of a pound of apples. The price of a pound of bananas is $0.10 less than double the price of apples. Joe bo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 980885: the price of a pound of cherries is $0.30 more than five times the price of a pound of apples. The price of a pound of bananas is $0.10 less than double the price of apples. Joe bought 4 pounds of cherries, 5 pounds of bananas, and 3 pounds of apples, and spent a total of $16.87. Find the price of apples, bananas and cherries.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the price in cents of a pound of cherries
Let +a+ = the price in cents of a pound of apples
Let +b+ = the price in cents of a pound of bananas
-----------------------------------------
(1) +c+=+5a+%2B+30+
(2) +b+=+2a+-+10+
(3) +4c+%2B+5b+%2B+3a+=+1687+
-----------------------------
This is 3 equations and 3 unknowns, so it's solvable
Substitute (1) and (2) into (3)
(3) +4%2A%28+5a+%2B+30+%29+%2B+5%2A%28+2a+-+10+%29+%2B+3a+=+1687+
(3) +20a+%2B+120+%2B+10a+-+50+%2B+3a+=+1687+
(3) +33a+=+1687+-+120+%2B+50+
(3) +33a+=+1617+
(3) +a+=+49+
and
(1) +c+=+5a+%2B+30+
(1) +c+=+5%2A49+%2B+30+
(1) +c+=+245+%2B+30+
(1) +c+=+275+
and
(2) +b+=+2a+-+10+
(2) +b+=+2%2A49+-+10+
(2) +b+=+98+-+10+
(2) +b+=+88+
----------------------
The price of a pound of cherries is $2.75
The price of a pound of apples is $.49
The price of a pound of bananas is $.88
----------------
check:
(3) +4c+%2B+5b+%2B+3a+=+1687+
(3) +4%2A2.75+%2B+5%2A.88+%2B+3%2A.49+=+16.87+
(3) +11+%2B+4.4+%2B+1.47+=+16.87+
(3) +16.87+=+16.87+
OK