Question

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

Answer 1

Hint: For answering this question we have been asked to find the four consecutive multiples of $5$ whose sum is $90$ . We will assume the four consecutive multiples as $5x,5\left( x+1 \right),5\left( x+2 \right)and5\left( x+3 \right)$ . And now we will equate the sum of these four to $90$ and then find the value of $x$ and then evaluate the value of the four consecutive multiples.

Complete step by step solution:
Now considering from the question we have been asked to find the four consecutive multiples of $5$ whose sum is $90$ .
Let us assume $5x,5\left( x+1 \right),5\left( x+2 \right) and 5\left( x+3 \right)$ the four consecutive multiples of $5$ .
Now we will add these four consecutive multiples and equate it to ninety.
We will get $5x+5\left( x+1 \right)+5\left( x+2 \right)+5\left( x+3 \right)=90$ .
By performing simple arithmetic basic calculations we can simplify the expression and evaluate the value of $x$ .
By simplifying we will have
$\begin{align}
  & 5x+5\left( x+1 \right)+5\left( x+2 \right)+5\left( x+3 \right)=90 \\
 & \Rightarrow 5\left( x+x+1+x+2+x+3 \right)=90 \\
 & \Rightarrow 4x+6=18 \\
 & \Rightarrow 2x+3=9 \\
\end{align}$
By further simplifying we will have
$\begin{align}
  & \Rightarrow 2x+3=9 \\
 & \Rightarrow 2x=6 \\
 & \Rightarrow x=3 \\
\end{align}$
Since the value of $x$ is $3$ . Hence the four consecutive multiples of $5$ whose sum is $90$ are $15,20,25,30$.

Note:
While answering this question we should be sure with our concepts we apply and the calculations we perform during the solution process. This is a very simple and easy question that can be answered in a short span of time and very few mistakes are possible. Similarly we can find different multiples of $5$ whose sum is a given number in the same process. This question involves few simple basic arithmetic calculations.