Question

model each scenario. see example 3 21. an amusement park attraction requires that a rider’s height be within 12 of 50 inches. model the situation and then indicate the range of heights a visitor can be to ride.

Explanation:

Step1: Define the variable

Let \( h \) represent the height of a rider in inches.

Step2: Translate the condition into an absolute value inequality

The rider's height must be within 12 inches of 50 inches. This means the distance between \( h \) and 50 is less than or equal to 12. In absolute value terms, this is \( |h - 50| \leq 12 \).

Step3: Solve the absolute value inequality (optional, if we want to find the range of \( h \))

To solve \( |h - 50| \leq 12 \), we consider two cases:

• Case 1: \( h - 50 \geq 0 \) (i.e., \( h \geq 50 \)). Then the inequality becomes \( h - 50 \leq 12 \), so \( h \leq 50 + 12 = 62 \). Combining with \( h \geq 50 \), we have \( 50 \leq h \leq 62 \).
• Case 2: \( h - 50 < 0 \) (i.e., \( h < 50 \)). Then the inequality becomes \( -(h - 50) \leq 12 \), which simplifies to \( -h + 50 \leq 12 \). Subtracting 50 from both sides gives \( -h \leq -38 \), and multiplying both sides by -1 (and reversing the inequality sign) gives \( h \geq 38 \). Combining with \( h < 50 \), we have \( 38 \leq h < 50 \).

Combining both cases, the range of \( h \) is \( 38 \leq h \leq 62 \). But the main model (the absolute value inequality) is \( |h - 50| \leq 12 \).

Answer:

The model for the rider's height \( h \) (in inches) is \( |h - 50| \leq 12 \), and the range of heights is \( 38 \leq h \leq 62 \) inches.