Question

The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.

Answer 1

Let the smaller number be 'x'. So, the larger number = x + 7.
ATQ:
⇒ 6x + (x + 7) = 77
⇒ 6x + x + 7 = 77
⇒ 7x + 7 = 77
Subtracting 7 from both sides, we get
⇒ 7x + 7 $-$ 7 = 77 $-$ 7
⇒ 7x = 70
Dividing both sides by 7, we get
⇒ $\frac{7x}{7}=\frac{70}{7}$
x = 10
Thus, the smaller number = x = 10, and the larger number = x + 7 = 10 + 7 = 17.
The two required numbers are 10 and 17.