Question

There are two different numbers. If we subtract a quarter of the smaller of them from both, we get numbers, one of which will be five times larger than the other. How many times is a larger number greater than the smaller one?

Answer 1

The larger number is four times greater than the smaller number once we perform the operation described in the problem.

Step-by-step explanation:

Let us denote the smaller number as s and the larger one as l. The problem states that if we subtract a quarter of the smaller number (s/4) from both numbers, the new value of the larger number becomes five times the new value of the smaller number.

So, the equations representing the situation are:

• l - (s/4) = 5*(s - (s/4))
• l - s/4 = 5s - 5s/4
• l - (s/4) = 4s/4

We simplify to find the ratio l/s.

• l = 5s - s
• l = 4s

Thus, the larger number l is four times greater than the smaller number s.