# How do you find four consecutive multiples of 5 whose sum is 90?

May 2, 2018

$15 , 20 , 25 , 30$

#### Explanation:

We know that the multiples' will add up to 90, so their average must be $\frac{90}{4}$, or $22.5$. Since there are an even number of multiples (4), none of them will touch the average, but they will be centered around it. Therefore, the multiples must be $15 , 20 , 25 , 30$
Check:
$15 + 20 + 25 + 30 = 90$

May 2, 2018

$15$, $20$, $25$ and $30$

#### Explanation:

Let the smallest number of the bunch be $x$,

$x + \left(x + 5\right) + \left(x + 5 + 5\right) + \left(x + 5 + 5 + 5\right) = 90$

Simplify,

$4 x + 30 = 90$

Subtract $30$ from both sides,

$4 x = 60$

Divide,

$x = 15$

Since the smallest number is $15$, the rest are as follows: $20$, $25$ and $30$.

May 2, 2018

The multiples are $\text{ "15," "20," "25," } 30$

#### Explanation:

Any multiple of $5$ can be written as $5 x$

The next multiple will be when $x$ increases by $1$

The sum of four consecutive multiples of $5$ is $90$

$5 x + 5 \left(x + 1\right) + 5 \left(x + 2\right) + 5 \left(x + 3\right) = 90$

$5 x + 5 x + 5 + 5 x + 10 + 5 x + 15 = 90$

$20 x + 30 = 90$

$20 x = 60$

$x = 3$

So the first multiple of $5$ is $5 \times 3 = 15$

The multiples are $\text{ "15," "20," "25," } 30$