# Question #7a137

Jan 23, 2018

The three numbers are $54$, $324$ and $154$.

#### Explanation:

Call the first number '$n$', then the second number is $6 n$ and the third is $n + 100$.

We know the total of the three numbers is $n + 6 n + n + 100 = 532$.

Collecting like terms, $8 n + 100 = 532$, then $8 n = 432$, so $n = \frac{432}{8} = 54$.

The second number is $6$ times $n$, so $6 \times 54 = 324$.

The third is $n + 100 = 154$.

Jan 23, 2018

54, 154, & 324

#### Explanation:

To solve this, we'll call the first number $x$ .
Using this variable, we can create equations for the remaining two equations.
The second number we'll call $y$. It is 6 times the first so
$y = 6 x$ .
The third number we'll call $z$. It is 100 more than the first so
$z = 100 + x$.
The sum of all three numbers is $x + y + z = 532$.
Substituting in our equations we get $x + \left(6 x\right) + \left(100 + x\right) = 532$ which simplifies to $8 x = 432$.
We get $x = 54$, $y = 6 \left(54\right) = 324$, and $z = 100 + 54 = 154$.