One fourth of a number is 10 less than two third of the number find the numbers

To find the number, let's represent it as 'x'.

According to the problem, "one fourth of a number is 10 less than two thirds of the number."
One fourth of the number can be expressed as (1/4)x.
Two thirds of the number can be expressed as (2/3)x.

We can write the equation as: (1/4)x = (2/3)x - 10.

To solve this equation, we need to get rid of the fraction. One way to eliminate the fractions is by multiplying the entire equation by the least common multiple (LCM) of the denominators, which in this case is 12.

Multiplying the equation by 12 gives us: 12 * (1/4)x = 12 * ((2/3)x - 10).

Simplifying the equation: 3x = 8x - 120.

Next, we need to isolate the variable, so let's move 8x to the left side by subtracting 8x from both sides: 3x - 8x = -120.

Combine like terms: -5x = -120.

Finally, divide both sides of the equation by -5: x = -120 / -5 = 24.

Therefore, the number is 24.

Direct translation of English to Math:

(1/4)x = (2/3)x - 10
12 times every term:
3x = 8x - 120
-5x = -120
x = 24

The number is 24

(there is only one number, how can you say,
"find the numbers" ? )