Question

A family is comparing different car seats. One car seat is designed for a child up to and including 3030 lb. Another car seat is designed for a child between 1515 lb and 4040 lb. A third car seat is designed for a child between 3030 lb and 100100 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 3838​-lb ​child?

Answer 1

To model the weight ranges for the car seats using compound inequalities, we can define each car seat as follows:

1. Car Seat A: Designed for a child up to and including 30 lb. \[ x \leq 30 \]

2. Car Seat B: Designed for a child between 15 lb and 40 lb. \[ 15 \leq x \leq 40 \]

3. Car Seat C: Designed for a child between 30 lb and 100 lb, inclusive. \[ 30 \leq x \leq 100 \]

Now, to determine which car seats are appropriate for a 38 lb child, we will evaluate each inequality with \(x = 38\):

1. Car Seat A: \[ 38 \leq 30 \quad (\text{False}) \] Inappropriate.

2. Car Seat B: \[ 15 \leq 38 \leq 40 \quad (\text{True for both parts}) \] Appropriate.

3. Car Seat C: \[ 30 \leq 38 \leq 100 \quad (\text{True for both parts}) \] Appropriate.

Conclusion: A 38 lb child is appropriate for Car Seat B and Car Seat C, but not appropriate for Car Seat A.