SOLUTION: How old are they? If Christine's and Martine's ages are added, the total is 51 years. If Christine were 6 years older and Martine were 3 years younger, the two women would be th

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Question 122773: How old are they?
If Christine's and Martine's ages are added, the total is 51 years. If Christine were 6 years older and Martine were 3 years younger, the two women would be the same age.
a)represent this situation by system of equations.
b)how old are the two women?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement
:
Let c = C's age now
Let m = M's age now
:
"If Christine's and Martine's ages are added, the total is 51 years."
c + m = 51
or
c = (51-m); use for substitution
:
"If Christine were 6 years older and Martine were 3 years younger, the two women would be the same age."
c + 6 = m - 3
c = m - 3 - 6
c = m - 9
:
a)represent this situation by system of equations.
we did
:
b)how old are the two women?
Substitute (51-m) for c in the equation: c = m - 9
51 - m = m - 9
51 + 9 = m + m
2m = 60
m = 60%2F2
m = 30 yrs old
then
51 - 30 = 21 yrs is c's age
:
Christine is 21 and Martini is 30
;
:
Check solution in the statement:
I If Christine were 6 years older and Martine were 3 years younger, the two women would be the same age.
21 + 6 = 30 - 3
27 = 27