The difference between two numbers is 7 six times the smaller plus the larger is 77 find the numbers

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

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.

Concept: Simple Linear Equations in One Variable

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