# Word Problems Exercises

### Example 1

The number of cookies Jen brings to a party is directly proportional to one fewer than the number of guests at the party. She's on the outs with one of the partygoers and doesn't want him to have a cookie. In fact, that's the whole reason she made cookies in the first place. For spite. If Jen brings 33 cookies to a party with 12 guests, what proportionality constant does Jen use to determine how many cookies to bring?

### Example 2

Translate the statement "*x* is inversely proportional to 2*y* with a constant of 6" into an equation.

### Example 3

The amount of time it takes to drive 100 miles is inversely proportional to your speed. If it took 1.5625 hours to drive 100 miles, how fast were you going? Also, were you able to talk your way out of that speeding ticket?

### Example 4

A rectangular box has a height of 1 foot. The length of the box is 8 divided by one more than twice the width of the box. If the volume of the box is 2 square feet, how wide is the box?

### Example 5

A wire is cut so the ratio between the lengths of the two pieces is 3:2. We hope you cut the blue wire, because cutting that red wire is bad news. Each piece of wire is used to form the outline of a square. What sort of bomb are you defusing, exactly? We question your methods. If the combined area of the squares is 1300 in^{2}, how many inches long was the wire?