Question

Mike packed an equal number of flashlights in each of x gift boxes. The number of compartments in each gift box was 3 more than the number of boxes. The number of flashlights in each compartment of a box was 2 more than the number of compartments in each box. The expression below shows the total number of flashlights that Mike packed in all the boxes: x(x + 3)(x + 5) Which expression shows the number of flashlights in each box?

Answer 1

`(x + 3)(x + 5)`

Explanation:

Given :

Mike packed an equal number of flashlights in each of x gift boxes.

The number of compartments in each gift box was 3 more than the number of boxes.

The number of flashlights in each compartment of a box was 2 more than the number of compartments in each box.

To Find: Which expression shows the number of flashlights in each box?

Solution :

Since we are given that there are x boxes

And we are also given that The number of compartments in each gift box was 3 more than the number of boxes.

⇒x+3

Thus no. of compartments in each box = x+3

We are also given that The number of flashlights in each compartment of a box was 2 more than the number of compartments in each box.

⇒x+3+2

⇒x+5

Thus the no. of flashlights in each box = x+5

The expression below shows the total number of flashlights that Mike packed in all the boxes: x(x + 3)(x + 5)

Since x box contains flashlights = x(x + 3)(x + 5)

So, 1 box contains flashlight
`=(x(x + 3)(x + 5))/(x)`

`=(x + 3)(x + 5)`

Hence The expression shows the number of flashlights in each box :

`(x + 3)(x + 5)`