Question

Solve the following problems using two variables.
(i) Sum of two numbers is 60. The greater number is 8 more than thrice the smaller number.
Find the numbers.

Answer 1

Let the smaller number be x and the greater number be y
According to the question, we have:
x + y = 60 ...(1)
and
y = 3x + 8
$\Rightarrow 3x-y=-8$ ...(2)
Adding (1) and (2), we get:
x + y = 60
3x $-$ y =$-$8
----------------------
4x = 52
$\therefore x=\frac{52}{4}=13$
Substituting the value of x in equation (1), we get:
13+ y = 60
⇒ y = 47
∴ The two numbers are 13 and 47.