Question

The difference of Billy and his Dad's age is 32. Billy's Dad is 6 less than three times Billy's age. How do you write an equation one could solve to find the age of Billy's Dad?

Answer 1

We'll call Billy's age `x`

Explanation:

Then his dad's age will be `x+32`

Billy's age times three is `3x`

Now Dad's age is `6` less than `3x`

Or Dad's age, expressed both ways:
`x+32=3x-6->` subtract `x` on both sides:
`cancelx-cancelx+32=3x-x-6->` add `6` to both sides:
`32+6=3x-x-cancel6+cancel6->`
`38=2x->x=38//2=19`

So Billy is `19`, his father is `19+32=51`.

Check: `3xx19-6=51`

Answer 2

Billy is `19` and his dad is `51`

Explanation:

First define the ages of the two people we are dealing with.

Billy is younger. Let' Billy's age be `x` years.
The dad's age is `x+32" "` (their ages differ by 32)

Three times Billys age is `3x`
The dad is 6 years younger than `3x`

Put this together in an equation.

`3x - 6 = x+32`

`3x-x = 32+6`

`2x = 38`

`x = 19" "larr` this is Billy's age.

Check: Billy is 19, his DAd is `19+32 = 51`

`3 xx 19 -6 = 57-6 = 51`

The answer is correct