Question

(a) customers of a certain credit card earn points for using the card. the table below shows the number of points earned for the amount spent.

number of points	30	70	90

choose the correct description.

• each dollar spent does not always earn the same number of points.
• each dollar spent appears to earn the same number of points.

predicted amount spent to earn 100 points: $\square$

Explanation:

Step1: Check points per dollar

For the first pair: $\frac{30}{3} = 10$ points per dollar.
For the second pair: $\frac{70}{7} = 10$ points per dollar.
For the third pair: $\frac{90}{9} = 10$ points per dollar.
So each dollar earns 10 points. Thus, the correct description is "Each dollar spent appears to earn the same number of points."

Step2: Predict amount for 100 points

Let $x$ be dollars spent for 100 points. Since points per dollar is 10, we have $\frac{100}{x} = 10$. Solving for $x$: $x = \frac{100}{10} = 10$.

Answer:

The correct description is "Each dollar spent appears to earn the same number of points."
Predicted amount spent to earn 100 points: $\$10$