SOLUTION: Katy is 5 years younger than Marg. In 4 years, four times Marg's age will equal 6 times Katy's age. How old is Katy now?

Question 100766: Katy is 5 years younger than Marg. In 4 years, four times Marg's age will equal 6 times Katy's age. How old is Katy now?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an algebra expression for each statement:
:
Katy is 5 years younger than Marg.
K = M - 5
:
In 4 years,
K + 4
and
M + 4
:
four times Marg's age will equal 6 times Katy's age.
4(M+4) = 6(K+4)
4M + 16 = 6K + 24
4M = 6K + 24 - 16
4M = 6K + 8
:
How old is Katy now?
Substitute (M-5) for K (From the 1st equation), find M
4M = 6(M-5) + 8
4M = 6M - 30 + 8
4M - 6M = -22
-2M = -22
M = 11 yrs old now
Then
K = M - 5
K = 11 - 5
K = 6 yrs is Katy now
:
Check solution using the statement:
"In 4 years, four times Marg's age will equal 6 times Katy's age."
4(15) = 6(10); confirms our solutions
:
Did this make sense to you? Any questions?

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