How can the number 45 be divided into two parts such that four times one part is 9 less than 5 times the other?
- 20,25
- 21,24
- 19,26
- None of these
Explanation
We know that:
- x + y = 45
- 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.
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