Question

I am thinking of two numbers. Three times to the first added to four times the second is 65, while four times the first added to three times the second is 61. What is the sum of the two numbers?

Answer 1

ANSWER:

• Sum of the two numbers = 18.

GIVEN:

• Three times of the first added to four times the second is 65.

• Four times the first added to three times the second is 61.

TO FIND:

• Sum of the two numbers.

ASSUMPTION:

• Let the two numbers are x and y respectively.

EXPLANATION:

3x + 4y = 65 --------> 1

4x + 3y = 61 ----------> 2

Add the two equations.

7x + 7 y = 126 ------------>3

Divide by 7 on both sides.

x + y = 18

HENCE SUM OF THE TWO NUMBERS IS 18 .

VERIFICATION:

Subtract the equations 1 and 2.

- x + y = 4 -----------> 4

Multiply equation 4 by 7

- 7x + 7y = 28 -----------> 5

Add equations 3 and 5

0x + 14y = 154

2y = 22

y = 11

Substitute y = 11 in equation 4

- x + 11 = 4

- x = - 7

x = 7

x + y = 7 + 11 = 18

HENCE VERIFIED.