Number Concepts-Integers (InterMath)

A man was hired to work for $3 a day, but on condition that for every day he was idle he should forfeit $1.50.

By the time he was paid, he had more idle days than working days.

How many total days were accounted for in his $33 salary?



$3 = work day x = number of work days
$1.50 = idle day y = number of idle days
$33 = total pay


3x - 1.50 y = 33

Using the guess and check method and the equation above,

I found that the number of working days could be 25 and the number of idle days could be 28, for a total of 53 days.

However, he can be idle for an even number of days over 26.

It must be even because he works whole days, not parts of days. An odd number of days would give you a remainder, which indicates parts of days.