Asif123 wrote:

3 years ago, Henry's age was six years more than twice the age of Mary. The average of their ages from that time and the present is 30 years. What would Mary’s age in years be in 5 years?time?

A. 25

B. 24

C. 29

D. 30

E. 45

3 years ago, Henry's age was six years more than twice the age of Mary.Let M = Mary's age THREE YEARS AGO

This means 2M + 6 = Henry's age THREE YEARS AGO

To find their PRESENT ages, we add three years to each age from THREE YEARS AGO

So M + 3 = Mary's PRESENT age

And 2M + 6 + 3 = Henry's PRESENT age

The average of their ages from that time and the present is 30 yearsThis means we need to add their ages from three years ago and their present ages

We get: \(\frac{M+(2M+6)+(M+3)+(2M+6+3)}{4 = 30}\)

Simplify: \(\frac{6M+18}{4 = 30}\)

Multiply both sides of the equation by 4 to get: \(6M+18=120\)

Subtract 18 from both sides: \(6M=102\)

Solve: \(M=17\)

So Mary was 17 THREE YEARS AGO

What would Mary’s age in years be in 5 years?From our above work we see that Mary's age THREE YEARS AGO was 17

This means her PRESENT age is 20

So, in five years, her age will be 25

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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