Question

Solve the following problems using two variables.
(ix) Sum of two numbers is 97. If the larger number is divided by the smaller, the quotient is 7 and the remainder is 1.
Find the numbers.

Answer 1

Let the larger number be x and the smaller number be y.
Then according to the question, we have:
x + y = 97 ...(1)
and
x = 7y + 1
⇒ x $-$ 7y = 1 ...(2)
Subtracting (1) from (2), we get:
x $-$ 7y = 1
x + y = 97
$-$ $-$ $-$
---------------------
$-$ 8y = $-$ 96
⇒ y = 12
Substituting the value of y in (1), we get:
x + 12 = 97
⇒ x = 85
∴ The numbers are 85 and 12.