Question

Three fourths a number plus 8 is 20 less than the number

Answer 1

Equation:
`(3)/(4)n+8=n-20`

Solve for n: n = 112

Explanation:

To first set up the equation, you need to look at the verbal description and translate into numbers and operations:

'three fourths a number' =
`(3)/(4) n`

'plus 8' = + 8

'is' =

'20 less' = - 20

'the number' = n

Put the expressions together:

'three fourths a number plus 8':
`(3)/(4)n+8`

'20 less than the number': n - 20

Set them equal to each other and solve:
`(3)/(4)n+8=n-20`

Add 20 to both sides:
`(3)/(4)n+8+20=n-20+20`

Subtract
`(3)/(4)n` from both sides:
`(3)/(4)n-(3)/(4)n+28=n-(3)/(4)n`

Multiply both sides by
`(4)/(1)`:
`(4)/(1)28=(1)/(4)n(4)/(1)`

Solve for n: n = 112