This problem is a checkpoint for solving problems by writing equations. It will be referred to as Checkpoint 8B.

For each problem, write one or two equations to represent the situation and then solve. Be sure to define your variable(s) and clearly answer the question.

1. The Lees have three children. The oldest is twice as old as the youngest. The middle child is five years older than the youngest. If the sum of their ages is $57$, how old is each child?

2. In Katy’s garden there are $105$ ladybugs. They are increasing by two ladybugs per month. There are currently $175$ aphids, and the number of aphids is decreasing at three aphids per month. When will the number of ladybugs and aphids in Katy’s garden be the same?

3. At the farmers’ market, Laura bought three pounds of heirloom tomatoes. If the tomatoes are priced at $$8$ for five pounds, what did Laura pay for her tomatoes?

4. Adult tickets for the school play cost $$5$ and student tickets cost $$3$. Thirty more student tickets were sold than adult tickets. If $$1770$ was collected, how many of each type of ticket were sold?

Check your answers by referring to the Checkpoint 8B materials located at the back of your book.

Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 8B materials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.