# Solving an Age Problem with a System of Linear Equations

by arif
(saudi arabia)

The sum of Mira and Shaheena is 40 years. After 10 years Mia will be twice as old as Shaheena. What is Mia's age. What is Shaheena's age?

Solution

Let m be Mira's age

Let s be Shaheena's age

The sum of Mira and Shaheena is 40 years.

The statement above gives the following equation

m + s = 40

After 10 years,

Mira's age will be m + 10

Shaheena's age will be s + 10

The problem also says that Mia will be twice as old as Shaheena.

The statement above gives the following equation

m + 10 = 2 × (s + 10)

m + 10 = 2 × s + 2× 10

m + 10 = 2s + 20

You now have a system of linear equation to solve

m + s = 40 equation 1

m + 10 = 2s + 20 equation 2

Use equation 1 to solve for m

m + s = 40

m + s - s = 40 - s

m = 40 - s

Replace 40 - s into equation 2

40 - s + 10 = 2s + 20

40 - s + s + 10 = 2s + s + 20

40 + 10 = 3s + 20

50 = 3s + 20

50 - 20 = 3s + 20 - 20

30 = 3s

Divide both sides by 3

30/3 = 3s / 3

10 = s

m + s = 40

m + 10 = 40

m + 10 - 10 = 40 - 10

m = 30

Shaheena is 10 years old. Mira is 30 years old

In 10 years Shaheena will be 20 and Mira will be 40. Mira's age will then be twice that of Shaheena.

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