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?

Oct 27, 2016

We'll call Billy's age $x$

Explanation:

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

Billy's age times three is $3 x$

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

Or Dad's age, expressed both ways:
$x + 32 = 3 x - 6 \to$ subtract $x$ on both sides:
$\cancel{x} - \cancel{x} + 32 = 3 x - x - 6 \to$ add $6$ to both sides:
$32 + 6 = 3 x - x - \cancel{6} + \cancel{6} \to$
$38 = 2 x \to x = 38 / 2 = 19$

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

Check: $3 \times 19 - 6 = 51$

Oct 27, 2016

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 $x + 32 \text{ }$ (their ages differ by 32)

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

Put this together in an equation.

$3 x - 6 = x + 32$

$3 x - x = 32 + 6$

$2 x = 38$

$x = 19 \text{ } \leftarrow$ this is Billy's age.

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

$3 \times 19 - 6 = 57 - 6 = 51$