Question

An art teacher has a jar containing b buttons to distribute to her class for a project. In order to give each in the class 6 buttons, she will need 18 more buttons. If she gives each child 5 buttons, she will have 4 left over. How many children are in the class

Answer 1

22

Explanation:

Given:

An art teacher has the total number of buttons =
`b`

1. In order to give each in the class 6 buttons, she will need 18 more buttons.

2. If she gives each child 5 buttons, she will have 4 left over.

Question asked:

How many children are in the class ?

Solution:

Let total number of children in the class =
`x`

As given that, 18 more buttons will be needed to give 6 buttons to each.

The equation will be:-

`b+18=6x\\b-6x=-18\ (equation\ 1)`

Also given that, If she gives 5 buttons to each, she will have 4 left over.

The equation will be:-

`b-5x=4\ (equation\ 2)`

Subtraction equation 2 from 1

`b-6x-(b-5x)=-18-4\\b-6x-b+5x=-22\\-6x+5x=-22\\-x=-22\\Minus\ canceled\ by\ minus\\x=22`

Hence, total number of children are 22.