Word problems on simple equations

Example 1

Ali bought a bus ticket for 450 shillings to travel to school and remained with 1,750 shillings. How much money did he have?

Solution

Let $y$ be the total amount of money Ali had before buying a ticket.

Therefore, the equation will be: $y - 450 = 1750$

Add 450 on both sides of the equation.

$y - 450 + 450 = 1750 + 450$

$y + 0 = 2200$

$y = 2200$

Therefore, Ali had 2,200 shillings.

Example 2

Rehema is 5 years older than Kemi. If the sum of their ages is 25 years, find their ages.

Solution

Form a simple equation by choosing any variable.

Let $x$ be the age of Kemi.

Note that Rehema is 5 years older than Kemi. Thus, add 5 to Kemi's age to get Rehema's age.

That is, Rehema's age = $x + 5$

So the simple equation is, $(x + 5) + x = 25$.

Collect the terms with variable and add them.

$x + x + 5 = 25$

$2x + 5 = 25$

Subtract 5 from both sides of the equation.

$2x + 5 - 5 = 25 - 5$

$2x + 0 = 20$

$2x = 20$

Divide both sides by 2 to get the value of $x$.

$\frac{2x}{2} = \frac{20}{2}$

$x = 10$

Therefore, Kemi's age is 10 years.

Rehema's age = $10 + 5 = 15$ years.

Example 3

The age of Furaha is $\frac{1}{2}$ of the age of her aunt. If the sum of their ages is 54 years, find their ages.

Solution

Let $x$ be the age of Furaha's aunt.

The age of Furaha = $\frac{1}{2}x$

But the sum of their ages is 54 years.

Thus, the simple equation is given by:

$x + \frac{1}{2}x = 54$

$\frac{2x + x}{2} = 54$

$\frac{3x}{2} = 54$

Multiply both sides of the equation by 2 to get:

$\frac{3x}{2} \times 2 = 54 \times 2$

$3x = 108$

Divide by 3 on both sides

$\frac{3x}{3} = \frac{108}{3}$

$x = 36$

Thus, the age of Furaha's aunt is 36 years. The age of Furaha is given by:

$\frac{1}{2}x = \frac{1}{2} \times 36 = 18$

Therefore, the age of Furaha is 18 years.