Students in a Science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?

Thinking through logically: each group needs 7 resistors (4 for the large circuit, 3 for the small circuit) and 3 capacitors (2 for large, 1 for small). That means the class will need more than twice as many resistors as capacitors.

Because there are 100 resistors and 70 capacitors, they’ll run out of resistors first. How many groups can use 7 resistors each before that supply of 100 is depleted?

100/7 = 14.2857… which means 7 goes into 100 a little more than 14 times, which means 14 groups can each have 7 resistors with a couple resistors left over. So the answer is 14.

(If you’re feeling paranoid, no shame in checking to make sure the groups will have enough capacitors, too. If 14 groups use 3 capacitors each, they’ll use 42 capacitors. That’s way less than 70, so all good.)