Question

The sum of two numbers is 21.3/4 of the numbers added to 2/3 of other give a sum of 15. Find the two numbers.

Answer 1

let the two number be x and y
x + y = 21 ---------------> 8x + 8y = 169
(3/4)x + (2/3)y = 15 ---> 9x + 8y = 180
subtract:
x = 12
then y = 9

Answer 2

a = first number

b = second number

The sum of two numbers is 21 means:

a + b = 21

Subtract a to both sides.

b = 21 - a

3 / 4 of the numbers added to 2 / 3 of other give a sum of 15 means:

3 a / 4 + 2 b / 3 = 15

Replace b by 21 - a in this equation.

3 a / 4 + 2 • ( 21 - a ) / 3 = 15

Multiply both sides by 12

3 • 3 a + 4 • 2 • ( 21 - a ) = 180

9 a + 8 • ( 21 - a ) = 180

9 a + 168 - 8 a = 180

a + 168 = 180

Subtract 168 to both sides.

a = 12

b = 21 - a = 21 - 12

b = 9

The two numbers are 12 and 9.

Check result:

a + b = 12 + 9 = 21

3 a / 4 + 2 b / 3 =

3 • 12 / 4 + 2 • 9 / 3 =

36 / 4 + 18 / 3 = 9 + 6 = 15