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3 years ago, Henry's age was six years more than twice the
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23 Feb 2020, 06:37
23 Feb 2020, 06:37
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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
A. 25
B. 24
C. 29
D. 30
E. 45
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: 3 years ago, Henry's age was six years more than twice the
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28 Feb 2020, 10:16
28 Feb 2020, 10:16
2
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
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 years
This 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
Re: 3 years ago, Henry's age was six years more than twice the
[#permalink]
01 Mar 2020, 02:25
01 Mar 2020, 02:25
2
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 years
This means we need to add their ages from three years ago and their present ages
We get: M+(2M+6)+(M+3)+(2M+6+3)4=30M+(2M+6)+(M+3)+(2M+6+3)4=30
Simplify: 6M+184=306M+184=30
Multiply both sides of the equation by 4 to get: 6M+18=1206M+18=120
Subtract 18 from both sides: 6M=1026M=102
Solve: M=17M=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
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 years
This means we need to add their ages from three years ago and their present ages
We get: M+(2M+6)+(M+3)+(2M+6+3)4=30M+(2M+6)+(M+3)+(2M+6+3)4=30
Simplify: 6M+184=306M+184=30
Multiply both sides of the equation by 4 to get: 6M+18=1206M+18=120
Subtract 18 from both sides: 6M=1026M=102
Solve: M=17M=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
