During Rachel’s birthday party, Rachel thinks about the ages of her parents and herself. Rachel says, “Hey Mom and Dad, together your ages add up to 100 years!” Her dad is surprised. “You’re right,”

Question

During Rachel’s birthday party, Rachel thinks about the ages of her parents and herself. Rachel says, “Hey Mom and Dad, together your ages add up to 100 years!” Her dad is surprised. “You’re right,” he says, “and your age and mine total 64 years.” Rachel replies, “And my age and Mom’s age total 58.” How old are Mom, Dad, and Rachel? Explain how you got your answer.

Answer 1

M+D = 100 = sum of Mom's and Dad's ages

D+R = 64 = sum of Dad's and Rachel's ages

M+R = 58 = sum of Mom's and Rache's ages

subtract 3rd equation from the 2nd

D-M = 6

add to 1st equation

2D = 106

D = 53 years old for Dad

M= 47 years old for Mom

R =11 years old for Rachel