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.
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
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