The sum of the two numbers is 80. The sum of 25% of the first number and 40% of the second is 23.

The sum of the two numbers is 80. The sum of 25% of the first number and 40% of the second is 23. Find these numbers.

Take two numbers A and B. It is known that:

A + B = 80;

We express B through A:

B = 80 – A;

Let C be 25% of the number A and D – 40% of the number B:

C = 0.25 * A;

D = 0.4 * B = 0.4 * (80 – A) = 32 – 0.4 * A;

By the condition of the problem:

C + D = 23;

Means:

0.25 * A + (32 – 0.4 * A) = 23;

0.25 * A – 0.4 * A = 23 – 32;

– 0.15 * A = – 9;

A = 9 / 0.15 = 60;

Next, we calculate B:

B = 80 – A = 80 – 60 = 20;

Verification:

0.25 * A + 0.4 * B = 0.25 * 60 + 0.4 * 20 = 15 + 8 = 23;

Answer: the first number is 80; the second number is 20