Question

irections: find 1 classmate to work with, if possible. 1. the table represents the relationship between the base length and the height of some parallelograms. both measurements are in inches. base length (inches) height (inches) 1 48 2 24 3 16 4 12 6 8 what is the relationship between the base length and the height of these parallelograms? 2. visitors to a carnival are invited to guess the number of beans in a jar. the person who guesses the correct number wins $300. if multiple people guess correctly, the prize will be divided evenly among them. what is the relationship between the number of people who guess correctly and the amount of money each person will receive?

Explanation:

Step1: Analyze parallelogram data

For the parallelograms, when base length $b = 1$ and height $h=48$, $b\times h=1\times48 = 48$; when $b = 2$ and $h = 24$, $b\times h=2\times24=48$; when $b = 3$ and $h = 16$, $b\times h=3\times16 = 48$; when $b = 4$ and $h = 12$, $b\times h=4\times12=48$; when $b = 6$ and $h = 8$, $b\times h=6\times8=48$. Since the product of base - length and height is constant ($48$), they are inversely proportional.

Step2: Analyze carnival - prize data

Let the number of people who guess correctly be $n$ and the amount of money each person receives be $m$. The total prize money is $T = 300$. We know that $m=\frac{300}{n}$, which means as $n$ increases, $m$ decreases and vice - versa. The product $n\times m=300$ (constant). So they are inversely proportional.

Answer:

1. The base length and the height of the parallelograms are inversely proportional.
2. The number of people who guess correctly and the amount of money each person receives are inversely proportional.