Determine who owes whom and how much they need to pay

Question

Sue and Jim go the the ekka. They ride the Mighty Mouse, then the Ferris Wheel, which costs $29. Sue pays for both of them. Then, after lunch, Jim pays for the two of them to go on the Gravitron and the Ferris Wheel, which costs $27. At night time, sue goes on Gravitron again (but Jim doesn't) and then both of them go on the Mighty Mouse. Jim pays $23 for these night time rides. at the end of the night, Jim and Sue decide to only pay for their rides. Determine who owes whom and how much they need to pay

Answer 1

Given:

2(M + F) = 29

2(G+F) = 27

G + 2M = 23

Sue = 2M + 2F + 2G 

Jim = 2M + 2F +G 

 

Solve: 

 

G+2M=23

G=23-2M

 

2(G+F)=27

G+F= 27/2

G= 13.5 - F

 

Set G = G:

 

13.5 - F = 23 - 2M

-F = 9.5 -2M

F= 2M - 9.5 

 

Combine:

 

2(M+F) = 29

2( M + (2M - 9.5))= 29

M + (2M - 9.5) = 14.5

M + 2M = 24

3M = 24

M=8 

 

Plug M=8 into other equations:

 

G= 23-2M

G= 23-2(8)

G= 23-16

G=7

 

(Let’s stop and check to make sure we are right)

 

G+2M = 23

7 + 2(8) = 23

23=23

 

continue plugging in: 

 

2(M+F) = 29

2(8+F) = 29 

8+F=14.5

F=6.5 

 

(check again)

 

2(G+F)=27 

2(6.5 + 7) = 27

27=27

 

So now we know that :

 

F= 6.5

G= 7

M= 8 

 

Sue = 2M+2F+2G

Sue = 2(8) + 2(6.5) 2(7)

Sue owes a total of $43.

But he paid a total of $29

 

 

Jim = 2M+2F+G

Jim = 2(8) +2(6.5) + 7

Jim owes a total of $36 

But he paid a total of $50

 

 

SO ... Sue will owe Jim money. 

 

50-36 = 14

 

Sue owes Jim $14.