Question 1118415: The present ages of Ali and Mike are in the ratio 5: 3. If Ali had been 7 years older
and Mike 7 years younger, the age of Ali would have been 3 times the age of Mike.
Find their present ages.
Found 3 solutions by josgarithmetic, Theo, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! a equals the age of ali now.
m equals the age of mike now.
the ratio of ali's age to mike's age now is 5/3.
you get a/m = 5/3.
cross multiply to get 3a = 5m
solve for a to get a = 5m/3.
if ali was 7 years older and mike 7 years younger, then ali's age would be 3 times mike's age.
the equation for this is a + 7 = 3 * (m - 7
simplify to get a + 7 = 3m - 21.
solve for a to get a = 3m - 28.
you have two equations that need to be solved simultaneously.
they are:
a = 5m/3
a = 3m - 28
since 5m/3 and 3m - 28 are both equal to a, then they are equal to each other and you get:
5m/3 = 3m - 28.
muiltiply both sides of this equation by 3 to get:
5m = 9m - 84
subtract 9m from both sides of this equation to get -4m = -84.
divide both sides of this equation by -4 to get m = 21.
that's mike's age now.
the ali's age to mike's age now is 5/3 and from that we derived a = 5m/3.
a = 5m/3 becomes a = 5 * 21/3 which becomes a = 5 * 7 which becomes a = 35.
ali's age now is 35 and mike's age now is 21.
the ratio of ali's age now to mike's age now is 35/21 which is equal to 5/3.
if ali was 7 years older, he would be 42.
if mike was 7 years younger, he would be 14
3 * 14 = 42.
solution looks good.
solution is:
ali's age now is 35 and mike's age now is 21.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! The present ages of Ali and Mike are in the ratio 5: 3. If Ali had been 7 years older
and Mike 7 years younger, the age of Ali would have been 3 times the age of Mike.
Find their present ages.
Let multiplicative factor be x
Then Ali’s and Mike’s ages are 5x and 3x, respectively
We then get: 5x + 7 = 3(3x – 7)
5x + 7 = 9x – 21
5x – 9x = - 21 – 7
– 4x = - 28
x, or multiplicative factor = 
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