Aquantity and its 2/3 are added together and from thesum 1/3 of the sum is subtracted, and 10 remains. what is the quantity?

the quantity is 9

Step-by-step explanation:

Let x represent the quantity.

A quantity and its 2/3 are added together. The 2/3 of the number is 2/3 × x = 2x/3

The sum of the quantity and its 2/3 would be

x + 2x/3 = (3x + 2x)/3 = 5x/3

From the sum, 1/3 of the sum is subtracted. 1/3 of the sum would be

1/3 × 5x/3 = 5x/9

Subtracting 1/3 of the sum from the sum, it becomes

5x/3 - 5x/9 = (15x - 5x)/9 = 10x/9

If the remainder is 10, it means that

10x/9 = 10

Crossmultiplying

10x = 9 × 10 = 90

x = 90/10

x = 9

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