How Old Are They?

Mary’s and Bob’s ages combined are twice Jane’s age. Mary is 8 years older than Bob. Jane’s age plus Bob’s age is 20 years. How old are they?
Source: NCTM Mathematics Teacher, September 2006

Solution
Let b,j, and m represent the ages of Bob, Jane, and Mary respectively.
b+m=2j\qquad (1)
m-b=8\qquad\; (2)
b+j=20\qquad\; (3)
Add Eq. (1) and Eq. (2)
b+m=2j
m-b=8
——————
2m=2j+8
m=j+4\qquad (4)
Add Eq. (2) and Eq. (3)
m-b=8
b+j=20
——————
m+j=28\quad\;\; (5)
Substitute the value of m in Eq. (4)  into Eq. (5)
(j+4)+j=28
2j=24
j=12
Jane’s age equals 12.
Substitute the value of Jane’s age into Eq. (4)
m=12+4=16
Mary’s age equals 16.
Substitute the value of Jane’s age into Eq. (3)
b+12=20
b=8
Bob’s age equals 8.

Answer: Bob is 8, Jane 12, Mary 16

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About mvtrinh

Retired high school math teacher.
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