Question

Mia, Jan, and Eva are sisters. Their combined ages are 44. Mia is 4 years older than Jan. Eva is 5 years younger than Jan. Which system of equations could be used to find Mia’s age?

Let x = Mia’s age, y=Jan’s age, and z=Eva’s age

Answer 1

Because of the question we know that Mia (x) is 4 years older (+ 4) than Jan (y) and Eva (z) is 5 years younger (- 5) than Jan:

x = y + 4
z = y - 5

Substitute:

x + y + z = 44
y + 4 + y + y - 5 = 44

Collect like terms:

3y + 4 - 5 = 44

Isolate 3y:

3y = 45

y = 15

Since we now know y (Jan’s age), we can find out Mia and Eva’s ages:

Mia: y + 14
= 15 + 4
Mia is 19 years old

Eva: y - 5
= 15 - 5
Eva is 10 years old

Proof:

x + y + z = 44
19 + 15 + 10 = 44