Question

Four-fifths of a number exceeds two-thirds of the number by 10 what is the number

Answer 1

Four-fifths of a number exceeds two-thirds of the number by 10. The number is 75

Solution:

Let the number be "x"

Given that,

Four-fifths of a number exceeds two-thirds of the number by 10

Here, "exceed" means that more than or addition

Therefore, we can say,

Four-fifths of a number = two-thirds of the number + 10

Writing it mathematically we get,

$\frac{4}{5} \times x = \frac{2}{3} \times x + 10\\\\\frac{4x}{5} = \frac{2x}{3} + 10\\\\\text{Move the variables to one side of equation }\\\\\frac{4x}{5} - \frac{2x}{3} = 10\\\\\text{Solve the above equation }\\\\\frac{4x \times 3}{5 \times 3} -\frac{2x \times 5}{3 \times 5} = 10\\\\\frac{12x-10x}{15} = 10\\\\2x = 150\\\\\text{Divide both sides of equation by 2}\\\\x = 75$

Thus the number is 75