Question

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

Answer 1

Answer:

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)

Substituting the eq. (iii) in eq. (ii) we will get,

6x+7+x=77

⇒7x=77-7

⇒x=\frac{70}{7}

⇒x=10

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

y=7+x=7+10=17

∴The smallest number 10 and the largest number is 17

Answer 2

$Smallest \: Number = x$

$largest \: number = y$

$A.T.Q$

$y - x = 7 \ \: \: \: \: \: \: \: (1)$

$6x + y = 77 \: \: \: \: \: \: (2)$

$From \: Eq \: 1$

$y = 7 + x \: \: \: \: \: \: (3)$

$substitute \: eq \: 3 \: in \: 2$

$6x + 7 + x = 77$

$7x = 77 - 7$

$7x = 70$

$x = \frac{70}{7}$

$x = 10$

$substitute \: x \: in \: eq \: (3)$

$y = 7 + 10 = 17$

$Smallest \: number = 10$

$largest \: number = 17$