Question

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

Answer 1

Let the smallest number = x

and the largest number = y

According to the condition,

y - x = 7 …(i)

and 6x + y = 77 ….(ii)

From eq. (i)

y = 7 + x …(iii)

Substitute the eq. (iii) in eq. (ii)

6x + 7 + x = 77

⇒ 7x = 77 - 7

⇒ x = `70/7 = 10`

Now, substitute the value of x in eq. (iii)

y = 7+ 10= 17

∴ The smallest number 10 and the largest number is 17.