## Five years ago, Nina was twice as old as Sam. In five years, she will be 1.5 times as old as Sam. How old are Nina and Sam now?

Question

Five years ago, Nina was twice as old as Sam. In five years, she will be 1.5 times as old as Sam. How old are Nina and Sam now?

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2 weeks 2021-09-28T13:05:24+00:00 2 Answers 0

age of Sam= 15 years

age of Nina  = 25 years

Step-by-step explanation:

Let  Nina’s age be X years

Let  Sam’s age be Y years

Five years ago Nina’s age will be X- 5 years

Five years ago Sam’s age will be Y- 5 years

Given in question

Five years ago, Nina was twice as old as Sam

writing it mathematically using X and Y we have

Nina’s age = 2 * Sam’s age

X- 5 = 2 *(Y- 5)

X = 2 *(Y- 5) + 5 = 2Y – 10 + 5 = 2Y – 5  _________________equation A

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Five years in future Nina’s age will be X+ 5 years

Five years ago Sam’s age will be Y+ 5 years

Given in question

In five years, she will be 1.5 times as old as Sam

writing it mathematically using X and Y we have

Nina’s age = 1.5 * Sam’s age

X+5 = 1.5 *(Y+ 5)

X = 1.5*(Y+5) -5 = 1.5Y +7.5 – 5 = 1.5Y +2.5  _________________equation B

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in equation A we have X = 2Y – 5

in equation B we have X = 1.5Y + 2.5

equating equation A and B  we have

2Y – 5 = 1.5Y +2.5

=> 2Y – 1.5Y = 2.5 + 5

=> 0.5Y = 7.5

=> Y = 7.5/0.5 = 15

from equation A we have

X = 2Y – 5  (substituting the value of Y = 15 in equation we have)

X = 2*15 – 5 = 25

Therefore age of Sam= 15 years

age of Nina  = 25 years