Last summer, Pat worked at a summer camp.
For each day that he worked, he earned $100 and he was not charged for food.
For each day that he did not work, he was not paid and he was charged $20 for food.
After 70 days, the money that he earned minus his food costs equalled $5440.
On how many of these 70 days did Pat work?
Pick one
Let be the number of days on which Pat worked.
On each of these days, he earned 100 and had no food costs, so he earned a total of 100x$ dollars.
Since Pat worked for of the 70 days, then he did not work on days.
On each of these days, he earned no money and was charged 20 for food, so was charged a total of 20(70-x)$ dollars for food.
After 70 days, the money that he earned minus his food costs equalled $5440.
Algebraically, we get .
Thus, or , which gives .
Therefore, Pat worked on 57 of these 70 days.
(An alternative approach would be to test each of the five given choices to see how much money Pat earns after food costs are deducted.)