Question

While catching fireflies, you and a friend decide to have a competition.

After $m$ minutes, you have $\left(3m+13\right)$ fireflies and your friend has $\left(4m+6\right)$ fireflies.

$a)$ How many fireflies are caught each minute during the competition?
$b)$ How many fireflies are caught before the competition starts?

Answer 1

Step-1: Finding the number of fireflies caught during the competition:

The competition remains for $m$ minutes long when flies are caught and counted.

Given,

For $m$ minutes,

I caught $\left(3m+13\right)$ fireflies

My friend caught $\left(4m+6\right)$ fireflies

Total fireflies caught at $m$ minutes is

$\Rightarrow \left(3m+13\right)+\left(4m+6\right)=7m+19$

Step-2: Finding the number of fireflies caught each minute during the competition:

The competition remains for $m$ minutes long when flies are caught and counted. This will be represented by variable terms.

Let $3m$ be the variable term for your café and $4m$ be the variable term for your friend.

Thus by adding both the terms we get

$3m+4m=7m$

Now, the number of flies per minute can be calculated as,

$\frac{7m}{m}=7files$

Therefore, $7files$ were caught in each minute.

Step-3:Finding the number of fireflies caught before the competition starts:

Total fireflies caught at $m$ minutes is $7m+19$

Before the competition starts $m=0$

$\Rightarrow 7\times 0+19=19$

Therefore,$19$ files were caught before the start of the competition.