Question

A family is comparing different car seats. One car seat is designed for a child up to and including 26 lb. Another car seat is designed for a child between 20 lb and 40 lb. A third car seat is designed for a child between 26 lb and 90 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 30​-lb ​child?

Answer 1

To model the weight ranges of each car seat with compound inequalities, we can define the weight of the child as \(x\). Here are the inequalities for each car seat:

1. Car Seat 1 (up to and including 26 lb): \[ x \leq 26 \]

2. Car Seat 2 (between 20 lb and 40 lb): \[ 20 < x < 40 \]

3. Car Seat 3 (between 26 lb and 90 lb, inclusive): \[ 26 \leq x \leq 90 \]

Now, let's determine which car seats are appropriate for a 30-lb child.

• For Car Seat 1: The condition \(x \leq 26\) does not hold when \(x = 30\). Therefore, Car Seat 1 is not appropriate.

• For Car Seat 2: The condition \(20 < x < 40\) holds for \(x = 30\) because \(30\) is greater than \(20\) and less than \(40\). Therefore, Car Seat 2 is appropriate.

• For Car Seat 3: The condition \(26 \leq x \leq 90\) also holds for \(x = 30\) since \(30\) is between \(26\) and \(90\). Therefore, Car Seat 3 is appropriate.

In conclusion, the appropriate car seats for a 30-lb child are Car Seat 2 and Car Seat 3.