SOLUTION: 4 times Alice's age plus 4 times Cindy's age equals 152, and 5 times Alice's age plus 3 times Cindy's age equals 140. What is each person's age?

Question 965870: 4 times Alice's age plus 4 times Cindy's age equals 152, and 5 times Alice's age plus 3 times Cindy's age equals 140. What is each person's age?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let a = Alice's age
let c = Cindy's age
;
Write an equation for each statement
:
4 times Alice's age plus 4 times Cindy's age equals 152,
4a + 4c = 152
simplify, divide by 4
a + c = 38
c = (38-a)
:
and 5 times Alice's age plus 3 times Cindy's age equals 140.
5a + 3c = 140
Replace c with (38-a)
5a + 3(38-a) = 140
5a + 114 - 3a = 140
5a - 3a = 140 - 114
2a = 26
a = 13 is Alice's age
Find c
c = 38 - 13
c = 25 is Cindy's age
:
:
Check solution in the first equation
4(13) + 4(25) = 152

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