Question

You have to travel $5$ miles to reach your school from your home. If $\frac{5}{4}$ miles of your journey is by bus and $\frac{2.5x}{3}$ miles by car, then find the value of $x$.

• A. 4.5

Answer 1

The correct option is A 4.5
Given:

Distance from home to school = $5$ miles

Distance traveled by bus = $\frac{5}{4}miles$

Distance traveled by car = $\frac{2.5x}{3}$

Total distance = Sum of the distance covered by bus and that by car

$5=\frac{5}{4}+\frac{2.5x}{3}$

$5=\frac{5\times 3+(2.5x\times 4)}{12}\text{LCM of 3, 4 is 12}$

By multiplying 12 on both sides, we get:

$5\times 12=15+10x$

$60=15+10x$

By subtracting 15 on both sides of the equation, we get:

$60-15=10x$

$45=10x$

Upon dividing by 10 on both sides, we get:

$x=\frac{45}{10}$

$x=4.5$

Therefore, the value of $x$ in the given equation is $4.5$.