## Bob is 25 years younger than his father and 27 years older than his son. Together, the sum of their ages is 100. What is each of

Question

Bob is 25 years younger than his father and 27 years older than his son. Together,
the sum of their ages is 100. What is each
of their ages?

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5 months 2021-08-26T19:56:36+00:00 2 Answers 6 views 0

Bob son is 7 years

Father’s age is 59 years

Bob is 34 years

Step-by-step explanation:

Bob age be x

Father age be y

Son’s age be w

Bob is younger means father is older;

y = 25+x ; x = y -25

x = 27 + w

y-25 = 27+w

y = 27+25+w = 52 +w

x + y + w = 100

27+w + 52+w +w = 100

79+3w = 100

3w = 100-79 = 21

w = 21/3 = 7 years

y = 52+w = 52+7 = 59 years

x = 27 + w = 27 +7 = 34 years

Bob = 34, father = 59, son = 7

Step-by-step explanation:

Use a system of equations:

Bob = x

Father = x + 25

Son = x – 27

Add them all together, set equal to 100 and solve:

x + x + 25 + x -27 = 100

3x – 2 = 100

3x = 102

x = 34 (bob)

Then plug x back into the equations to solve for father and son age:

34 + 25 = 59 (father)

34 – 27 = 7 (son)

Then you can check your work by adding 34+59+7 and you get 100.