SOLUTION: Nina is 5 years younger than Fred. In 6 years, Nina will be three-fourths as old as Fred. How old is Fred now?

Question 620303: Nina is 5 years younger than Fred. In 6 years, Nina will be three-fourths as old as Fred. How old is Fred now?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Nina = n
Present age of Fred = f

Nina is 5 years younger than Fred.
n=f-5.............(1)

In 6 years,
Nina will be = n+6
Fred will be = f+6

Then
Nina will be three-fourths as old as Fred
(n+6)=3/4(f+6)
4(n+6)=3(f+6)
4n+24=3f+18
4n=3f+18-24
4n=3f-6....................(2)

Substitute the value of n from (1) to (2)
4(f-5)=3f-6
4f-20=3f-6
4f-3f=-6+20
f=14

Substitute the value of f in (1)
n=f-5
n=14-5
n=9

Present age of Nina = n = 9 years old
Present age of Fred = f = 14 years old

Check
-----
In 6 years Fred will be = 14+6 = 20
In 6 years Nina will be = 9+6 = 15 (which is 3/4 of 20, 20(3/4)=60/4=15)

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