Question

Let the function $f$ be defined by $f\left(x\right)=5x-2a$, where $a$ is a constant. If $f\left(10\right)+f\left(5\right)=55$, what is the value of $a$?

• A. -5
• B. 0
• C. 5
• D. 10
• E. 20

Answer 1

The correct option is C 5

Given, $f\left(x\right)$ $=$ $5x$ $-$ $2a$ and $f\left(10\right)$ $+$ $f\left(5\right)$ $=$ $55$

$\Rightarrow f\left(10\right)$ $=$ $5$ $\times$ $10$ $-$ $2a$

$\Rightarrow f\left(10\right)$ $=$ $50$ $-$ $2a$ .... (1)

$\Rightarrow f\left(5\right)$ $=$ $5$ $\times$ $5$ $-$ $2a$

$\Rightarrow f\left(5\right)$ $=$ $25$ $-$ $2a$ .... (2)

On adding equations (1) and (@), we get

$f\left(10\right)$ $+$ $f\left(5\right)$ $=$ $50$ $-$ $2a$ $+$ $25$ $-$ $2a$

$\Rightarrow 55$ $=$ $75$ $-$ $4a$

Rearranging the terms, we get

$4a$ $=$ $75$ $-$ $55$

$\Rightarrow 4$ $\times$ $a$ $=$ $20$

$\Rightarrow a$ $=$ $\frac{20}{4}$

$\Rightarrow a$ $=$ $5$

Therefore, the value of ${}^{\prime }{a}^{\prime }$ is $5$.