Question

a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 find the number

Answer 1

$\frac{x}{5} + 5 = \frac{x}{4} - 5 \\ \frac{x + 25}{5} = \frac{x - 20}{4 } \\ 5(x - 20) = 4(x + 25) \\ 5x - 100 = 4x + 100 \\ 5x - 4x = 100 + 100 \\ x = 200 \\ \\ number = \frac{x + 25}{5} \\ \frac{200 + 25}{5 } \\ \frac{225}{5 } \\ 45$

Answer 2

x/5+5=x/4-5
x/4-x/5=5+5
(5x-4x)/20=10
x/20=10
x=200