Question

The expression $ax+b$ is equal to $13$ when $x$ is $5$ and to $25$ when $x$ is $13$. Find the value of the expression when $x$ is $0.5$

• A. $7.55$
• B. $9.23$
• C. $6.33$
• D. $6.25$

Answer 1

The correct option is D $6.25$

Given, $ax+b=13$ when $x=5$

$=>5a+b=13$ --- (1)

Also, $ax+b=25$ when $x=13$

$=>13a+b=25$ --- (2)

Subtracting equation $\left(1\right)$

from $\left(2\right)$, we get $8a=12=>a=\frac{3}{2}$

Substituting $a=\frac{3}{2}$ in the equation $\left(1\right)$, we get $\frac{15}{2}+b=13=>b=\frac{11}{2}$

So, value of $ax+b$ when $x=0.5$ is $\frac{3}{2}\times 0.5+\frac{11}{2}=6.25$