Question

The number of Mathematics teachers at a school is `5` more than `4` times the number of English teachers. The school has `100` Mathematics and English teachers in all. How many Mathematics and English teachers work at the school?

Answer 1

There are `19` English teachers and `81` Maths teachers,

Explanation:

We can solve this problem using only one variable because we know the relationship between the number of Maths and English teachers,

There are fewer English teachers so let that number be `x`

The number of Maths teachers is `5` more than (this means add `5`)
`4` times (this means multiply by `4`) the English teachers (`x`.)

The number of Maths teachers can be written as; `4x +5`

There are `100` Maths and English teachers altogether.
Add the numbers of teachers together.

`x+4x+5 = 100`
`color(white)(wwwww)5x = 100-5`
`color(white)(wwwww)5x = 95`
`color(white)(w.wwww)x = 19" "larr` the number of English teachers.

There are `4 xx 19 +5 = 81` Maths teachers,

Check: `19+81 = 100`