Question

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

Answer 1

Answer- The above question is from the chapter 'Pair of Linear Equations in Two Variables'.

Let two numbers be x and y such that x> y.

First condition: The difference between two numbers is 7.

x - y = 7  ---- (1)

⇒ x = y + 7

Second condition: Six times the smaller number plus the larger number is 77.

6y + x = 77 ---- (2)

Put value of x from equation 1 in equation 2.

6y + y + 7= 77

7y +7 = 77

Transposing 7 to RHS,

7y = 77 - 7

7y = 70

y = 10

Put value of y = 10 in equation 1,

x - 10 = 7

Transposing 10 to RHS,

x = 7 + 10

x = 17

This method is called substitution method.

∴ x = 17 and y = 10

∴ Required two numbers are 17 and 10.

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Two \: numbers = 10 \: \& \: 17 }}}}$

$\rule{100}2$

Let the larger number be a & smaller number be b.

1st case:-

⇒ a - b = 7

⇒ a = b + 7 .................(eq.1)

2nd case:-

⇒ 6b + a = 77

• Putting value of a from (eq.1):-

$\sf {\: \: \: \: \:\: [\because a = b + 7]}$

⇒ 6b + b + 7 = 77

⇒ 7b + 7 = 77

⇒ 7b = 77 - 7

⇒ 7b = 70

⇒ b = 70/7

⇒ b = 10

$\therefore{\underline{\boxed{\rm{Smaller \: number = 10}}}}$

$\rule{100}{2}$

• Putting value of b in (eq.1):-

⇒ a = 10 + 7

⇒ a = 17

$\therefore{\underline{\boxed{\rm{Larger \: number = 17}}}}$