SOLUTION: Nine cartons of juice cost the same as 5 fruit cups. Also, one fruit cup costs $.50 more than a bowl of soup, while a bowl of soup costs $.50 more than a carton of juice. What woul

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Question 227707: Nine cartons of juice cost the same as 5 fruit cups. Also, one fruit cup costs $.50 more than a bowl of soup, while a bowl of soup costs $.50 more than a carton of juice. What would be the cost of each item: a carton of juice, a fruit cup, and a bowl of soup?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let j= cost of a carton of juice
Let f= cost of a fruit cup
Let s= cost of a bowl of soup
given:
(1) 9j+=+5f
(2) f+=+s+%2B+50 (in cents)
(3) s+=+j+%2B+50 (in cents)
-----------------
Rewrite equations
(1) j+=+%285%2F9%29%2Af
(2) f+-+s+=+50
(3) -j+%2B+s+=+50
Add (2) and (3)
f+-+j+=+100
Substitute (1) in this equation
f+-+%285%2F9%29%2Af+=+100
%284%2F9%29%2Af+=+100
4f+=+900
f+=+225
and, since
(2) f+-+s+=+50
225+-+s+=+50
s+=+175
And
(3) -j+%2B+s+=+50
-j+%2B+175+=+50
j+=+175+-+50
j+=+125
A carton of juice costs $1.25
A fruit cup costs $2.25
A bowl of soup costs $1.75
check:
9j+=+5f
9%2A125+=+5%2A225
1125+=+1125
OK