SOLUTION: 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 thei

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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): You can put this solution on YOUR website!




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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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