25% of the sum of numbers A and B is equal to 125% of the difference between numbers A and B.

25% of the sum of numbers A and B is equal to 125% of the difference between numbers A and B. Find the sum of the numbers A and B if the difference between three times the number A and half of B is 125.

Let’s write a system of two equations.

(a + b) * 0.25 = 1.25 * (a – b);

3 * a – 0.5 * b = 125.

0.25 * a + 0.25 * b = 1.25 * a – 1.25 * b;

3 * a – 0.5 * b = 125.

– a + b = 0;

Let us express the value of a through b and substitute it into the second equation.

a = b;

3 * b – 0.5 * b = 125.

b = 125 / 2.5 = 50.

a = 50.

a + b = 50 + 50 = 100.

Answer: the sum of numbers a and b is 100.