A number whose fifth part increased by 5 is equal to its third part decreased by 7. Find half of the number.

Question

Accepted Answer

Let the number be x.

According to the problem, the fifth part of the number increased by 5 equals the third part decreased by 7.

This can be written as:
(x/5) + 5 = (x/3) - 7

Bring all terms involving x to one side and constants to the other:
(x/5) - (x/3) = -7 - 5

Find common denominator for the left side:
(3x - 5x) / 15 = -12

Simplify numerator:
(-2x) / 15 = -12

Multiply both sides by 15:
-2x = -12 * 15
-2x = -180

Divide both sides by -2:
x = 90

The number is 90.

Half of the number = 90 / 2 = 45.

Therefore, the correct answer is 45.

Answer

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