Question

The sum of two consecutive multiples of 6 is 66. Find these multiples.

Answer 1

Hint: To solve this question, we will consider a variable for a multiple of 6. The multiples are consecutive and hence if we know one multiple, the other multiple will have a numerical value of 6 more than the original multiple. Thus, we will add the multiples and find the value of our variable. Once we are able to find the variable, we can add 6 to it to find the next variable.

Complete step-by-step answer:
Let the smaller of the two multiples of 6 be x and let the bigger multiple of 6 be y.
It is given that the sum of the two multiples is 66.
Thus, x + y = 66
We know that the difference between two consecutive multiples of 6 is 6.
Therefore, y – 6= x
Thus, y = x + 6
Thus, the bigger multiple has a numerical value of 6 more than the smaller multiple.
Now, we shall substitute y = x + 6 in the equation x + y = 66.
Thus, x + x + 6 = 66
$\Rightarrow $ 2x = 66 – 6
$\Rightarrow $ 2x = 60
$\Rightarrow $ x = 30
So, to find the value of y, we will substitute x = 30 in x + y = 66.
$\Rightarrow $ 30 + y = 66
$\Rightarrow $ y = 66 – 30
$\Rightarrow $ y = 36
Therefore, the two multiples of 6 whose sum is 66 are 30 and 36.

Note: Students are advised to check their answers after solving it, whether it is complying with the conditions or not. The answers, 30 and 36 are indeed multiples of 6 and their sum is indeed 66.