Question

Vij is developing a weight loss regimen, which includes both a workout plan and a calorie-restriction plan. Vij wants to work out for no less than $30$ minutes and no more than $60$ minutes a day and consume no less than $2,000$ and no more than $2,500$ calories. If each minute, m, of his workout time burns $50$ calories, which of the following inequalities represents the number of minutes, $m$, that Vij can work out each day to burn off as many calories as he consumes?

• A. $30\le m\le 60$
• B. $30\le m\le 50$
• C. $40\le m<50$
• D. $40\le m\le 50$

Answer 1

The correct option is D $40\le m\le 50$

Let $m$ be the time Vij is going to do work out

Given $30\le m\le 60$

For each minute $50$ calories will burn, so if Vij do work out for $m$ minutes then $50m$ calories will burn

The calories Vij is consuming per day is between $2000$ and $2500$

For calories spent on a day to be equal to calories consumed , the condition is

$\Rightarrow 2000\le 50m\le 2500$

$\Rightarrow 40\le m\le 50$