Question

Jason got an allowance of $\$20$. He wants to save more than $\$5$ at the end of $10$ days. He spends an equal amount of money everyday. Which of the following is true?

• A. Jason should spend less than $\$1.50$ daily.
• B. Jason should spend more than $\$1.50$ daily.
• C. Jason should spend less than or equal to $\$1.50$ daily.

Answer 1

The correct option is A Jason should spend less than $\$1.50$ daily.

Let the amount of money spent each day = $x$ dollars.

Initially Jason had $\$20$.

In $10$ day, total money spent by him = $10x\text{dollars}$

After $10$ days the amount of money left with Jason = $20-10x\text{dollars}$

He wants to save more than $\$5$ after 10 days.
$\therefore$ The amount of money saved is greater than $\$5$.
$\Rightarrow 20-10x>5$

Subtracting $20$ from both side of the inequality we get,

$20-10x>5-20=-20-10x>-15$

To undo the multiplication, we divide both side of the inequality by $-10$. This will reverse the inequality sign.
$-10x>-15$
$\Rightarrow \frac{-10x}{-10}<\frac{-15}{-10}$
$\Rightarrow x<1.5$

$\therefore$ Jason should spend less than $\$1.50$ each day to save more than $\$5$ at the end of $10\text{days.}$