Question

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

Answer 1

Given :-

• Difference b/w two numbers = 7
• Six times smaller + larger = 77

To find :-

• Find the numbers.

Solution :-

Let the smaller number be y & larger number be x

Case l :

→ x - y = 7

→ x = y + 7 ------ Equation (1)

Case 2 :

→ 6y + x = 77

Putting value from Equation (1)

→ 6y + y + 7 = 77

→ 7y + 7 = 77

→ 7y = 77 - 7

→ 7y = 70

→ y = 70/7

→ y = 10

So, smaller number = 10

Putting value in Equation (1)

→ x = 10 + 7

→ x = 17

So, larger number = 17

Therefore,

Two numbers are 17 & 10 .

$\rule{200}{1}$

Verification :-

→ 6 × Smaller + Larger = 77

Putting values of x & y

→ 6 × 10 + 17 = 77

→ 60 + 17 = 77

→ 77 = 77

∴ L.H.S. = R.H.S. [Hence verified!]

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the smaller number be x.

And the larger number be x + 7.

According to the Questions,

⇒ 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

⇒ 7x  = 707                          

⇒  x = 10

Smaller number = x = 10

Larger number = x + 7 = 10 + 7 = 17.

Hence,  the two numbers are 10 and 17.