1/4 of a certain number is added to 4 1/3. The sum is the same as when 1/3 of it is subtracted from 20 2/3. Find the number

Answer 1

x = number

x / 4 + 4 1/3 = 20 2/3 - x / 3

x / 4 + 4 + 1 / 3 = 20 + 2 / 3 - x / 3

x / 4 + 12 / 3 + 1 / 3 = 60 / 3 + 2 / 3 - x / 3

x / 4 + 13 / 3 = 62/ 3 - x / 3

Add x / 3 to noth sides.

x / 4 + x / 3 +13 / 3 = 62 / 3

Subtract 13 / 3 to both sides.

x / 4 + x / 3 = 49 / 3

3 • x / 3 • 4 + 4 • x / 4 • 3 = 49 / 3

3 x / 12 + 4 x / 12 = 49 / 3

7 x / 12 = 49 / 3

Cross multiply.

7 x • 3 = 12 • 49

21 x = 588

x = 588 / 21

x = 21 • 28 / 21

x = 28

The number is 28.