The sum of two sevenths and four sevenths is 24. And the difference between three fifths

The sum of two sevenths and four sevenths is 24. And the difference between three fifths and one fifth of another number is 40. How much is the first number less than the second?

Let’s denote the first number by x, and the second number by y.

According to the condition of the problem, the sum of two sevenths and four sevenths of the first number is 24, therefore, we can compose the following equation:

(2/7) * x + (4/7) * x = 24.

We solve the resulting equation:

(6/7) * x = 24;

x = 24 / (6/7);

x = 24 * (7/6);

x = 7 * 24/6;

x = 7 * 4;

x = 28.

It is also known that the difference between three-fifths and one-fifth of another number is 40, therefore, we can draw up the following equation:

(3/5) * y – (1/5) * y = 40.

We solve the resulting equation:

(2/5) * y = 40;

y = 40 / (2/5);

y = 40 * (5/2);

y = 5 * 40/2;

y = 5 * 20;

y = 100.

Find how much the first number is less than the second:

y – x = 100 – 28 = 72.

Answer: the first number is 72 less than the second.