Question

A box of candy contains three times as many cherry pieces. It hasfour more grape pieces than cherry pieces. There are 46 total pieces in the box. How many cherry pieces are in the box

Answer 1

The number of cheery pieces in the box are
`18`.

Explanation:

Let the number of orange pieces in the box be
`x`.

The box contains three times as many cherry pieces as orange pieces.

So, the number of cherry pieces in the box be
`3x`.

It has four more grape pieces than cherry pieces.

So, the number of grape pieces in the box be
`3x+4`.

There are
`46` total pieces in the box.

So,
`x+3x+3x+4=46`

`\Rightarrow 7x+4=46`

`\Rightarrow 7x=46-4`

`\Rightarrow 7x=42`

`\Rightarrow x=(42)/(7)`

`\Rightarrow x=6`

So, the number of cherry pieces
`=3x=3* 6=18`.

Hence, the number of cheery pieces in the box are
`18`.