Question

Carlos buys a box of frozen flavored ice sticks. 2/5 of the ice sticks are blue raspberry. Of the remaining ice sticks, 1/3 are grape, and the rest are cherry. If there are 48 blue raspberry and cherry flavored ice sticks altogether, how many ice sticks total are in the box?

Answer 1

Given:

$\dfrac{2}{5}$ of the ice sticks are blue raspberry.

Of the remaining ice sticks, $\dfrac{1}{3}$ are grape, and the rest are cherry.

There are 48 blue raspberry and cherry flavored ice sticks altogether.

To find:

The total number of ice sticks.

Solution:

Let x be the total number of ice sticks.

$\dfrac{2}{5}$ of the ice sticks are blue raspberry.

Blue raspberry $=\dfrac{2}{5}x$

Remaining raspberry $=x-\dfrac{2}{5}x$

                                   $=\dfrac{3}{5}x$

Of the remaining ice sticks, $\dfrac{1}{3}$ are grape, and the rest are cherry.

Grape $=\dfrac{1}{3}\times \dfrac{3}{5}x$

          $=\dfrac{1}{5}x$

Cherry $=\dfrac{3}{5}x-\dfrac{1}{5}x$

           $=\dfrac{2}{5}x$

There are 48 blue raspberry and cherry flavored ice sticks altogether.

$\dfrac{2}{5}x+\dfrac{2}{5}x=48$

$\dfrac{4}{5}x=48$

$x=48\times \dfrac{5}{4}$

$x=60$

Therefore, the total number of ice sticks is 60.