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,
[tex]\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[/tex]
Thus the number is 75
