total cost of items

Question

Nine cartons of juice cost the same as 5 fruit cups. Also, one fruit cup costs $0.50 more than one bowl of soup, while one bowl of soup costs $0.50 more than one bowl of soup, while one bowl of soup costs $0.50 more than one carton of juice., a fruit cup, and a bowl of soup.

Answer 1

carton of juice, J

fruit cup, F

bowl of soup, S

 

9J = 5F

 

F = S + 0.50

 

S = J + 0.50

 

substituting the third equation into the second equation:

 

F = J + 0.50 + 0.50 = J + 1

 

Now there are two equations and 2 unknowns:

 

9J = 5F

 

F = J + 1

 

9J = 5(J + 1)

9J = 5J + 5

 

4J = 5

 

J = 5/4 = $1.25

 

F = $2.25

 

S = $1.25 + 0.50 = $1.75

 

fruit cup costs $2.25

1 carton of juice costs $1.25

1 bowl of soup costs $1.75.

 

Note that 9 x 1.25 = 11.25 = 5 x 2.25 <---9 cartons of juice cost the same a 5 fruit cups.