SOLUTION: The Smith family pays $60 for 4 adult meals and 1 kid's meal. The Jones family pays $42 for 2 adult meals and 2 kid's meals. How much was each adult meal and each kid's meal.

Question 169162: The Smith family pays $60 for 4 adult meals and 1 kid's meal.
The Jones family pays $42 for 2 adult meals and 2 kid's meals.
How much was each adult meal and each kid's meal.
Here is what I have so far . . .
4x + y = 60
+ 2x + 2y = 42
_______________
6x + 3y = $102

Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The Smith family pays $60 for 4 adult meals and 1 kid's meal.
The Jones family pays $42 for 2 adult meals and 2 kid's meals.
How much was each adult meal and each kid's meal.
Here is what I have so far . . .
4x + y = 60
+ 2x + 2y = 42
_______________
6x + 3y = $102
-----------------
4x + y = 60
2x + 2y = 42 Divide this one by 2
x + y = 21 Subtract this one from the 1st one, the Smiths
3x + 0y = 39
x = 13
The idea is to multiply one of the eqns so that one variable has the same coefficient. Then you can add or subtract to eliminate that variable. What you did is correct, but it didn't help.
Adult meal = $13
Kids' meal = $8

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The Smith family pays $60 for 4 adult meals and 1 kid's meal.
The Jones family pays $42 for 2 adult meals and 2 kid's meals.
How much was each adult meal and each kid's meal.
Here is what I have so far . . .
4x + y = 60
2x + 2y = 42
:
These are the right equations, but you want to multiply one or both equations,
so that you can eliminate one of the variables.
:
In this case if we multiply the 1st equation by 2 and subtract we eliminate y
8x + 2y = 120
2x + 2y = 42
--------------- subtraction eliminates y, find x
6x + 0 = 78
x =
x = $13 for adult meal
:
Use the 1s equation to find y, substitute 13 for x:
4(13) + y = 60
52 + y = 60
y = 60 - 52
y = $8 for kids meal
;
;
Check solution in the 2nd equation
2(13) + 2(8) = 42
26 + 16 = 42, confirms our solutions
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