How can the number 45 be divided into two parts such that four times one part is 9 less than 5 times the other?

How can the number 45 be divided into two parts such that four times one part is 9 less than 5 times the other?

Explanation

We know that:

  1. x + y = 45
  2. 4x = 5y - 9

From the first equation, we can express y in terms of x:

y = 45 - x

Substitute this into the second equation:

4x = 5(45 - x) - 9

Expand and simplify:

4x = 225 - 5x - 9

9x = 216

x = 24

Now, substitute x = 24 into the first equation:

24 + y = 45

y = 21

Therefore, the two parts are 24 and 21.