Find the number such that when 3/4 of it is added to 3and the half , the sum is the same as when 2/3 of it is subtracted from 6 and 1/2.
x = number
3 / 4 x + 3 1/2 = 6 1/2 - 2 / 3 x
3 x / 4 + 3 + 1 / 2 = 6 + 1 / 2 - 2 x / 3
3 x / 4 + 6 / 2 + 1 / 2 = 12 / 2 + 1 / 2 - 2 x / 3
3 x / 4 + 7 / 2 = 13 / 2 - 2 x / 3
Add 2 x / 3 to both sides.
3 x / 4 + 2 x / 3 + 7 / 2 = 13 / 2
Subtract 7 / 2 to both sides.
3 x / 4 + 2 x / 3 = 6 / 2
3 x / 4 + 2 x / 3 = 3
3 • 3 x / 3 • 4 + 4 • 2 x / 4 • 3 = 3
9 x / 12 + 8 x / 12 = 3
17 x / 12 = 3
Multiply both sides by 12.
17 x = 36
x = 17 / 36
The number is 17 / 36