System of equations word problem

Question

Tammy's age is the sum of the ages of Carmen and Dennis. Carmen's age is 2 more than the sum of the ages of Dennis and Mark. Dennis's age is 4 times Mark's age. The sum of all four ages is 42. What is Tammy's age?

Answer 1

Let the first letter of each name represent the age of that person

T + C + D + M = 42

T = C + D

C + D + M + 2

D = 4M

C = 4M + M + 2 = 5M + 2

T = 5M + 2 + 4M = 9M + 2

Substitute in the sum equation

9M +2 + 5M +2 + 4M + M = 42

19M + 4 = 42

19M = 38

M = 2

D = 8

C =12

T = 20

This set of equations reminds you of one important fact: in order to solve a set of linear equations, there must be as many equations as there are unknowns!