Some problems require you to determine if a calculation, estimation, or conclusion is reasonable.

Example 1

Carson plans to go roller-skating this summer. The cost to rent or buy the skates is shown in the table below.

He believes that it would cost less to rent the skates than to purchase them since he plans to skate exactly 6 days this summer. Is Carson's conclusion reasonable?

Source: Roller skates, Indy Charlie, Flickr

Yes, because if x represents the number of days the skates are rented, then 3.25x < 20, and 3.25(6) < 20, or 19.50 < 20.

Therefore, Carson’s conclusion is reasonable. It is less expensive to rent the skates for 6 days than to buy them.

Example 2

Mr. Whitton plans to buy party favors online for his son’s birthday party. The favors cost $2.00 each and the shipping charge is $4.50, regardless of the number of favors ordered.

Mr. Whitton budgeted $35.00 for the party favors. He believes that the maximum number of party favors he can order is 16. Is his conclusion reasonable?

No, because if x represents the number of party favors and the budget is $35, then the inequality would be set up as 2.00x + 4.50 ≤ 35. With 16 favors ordered, 2.00(16) + 4.50 ≤ 35, or 36.50 ≤ 35 which is not a true statement.

If Mr. Whitton only ordered 15 party favors, then 2.00(15) + 4.50 ≤ 35, or 34.50 ≤ 35 which is a true statement. Therefore, the maximum number of party favors he can order and stay within his budget is 15.

1. Click Start.
2. For each problem, click on the most reasonable solution.
3. Click either Next (correct) or Try Again (incorrect).