Question

the graph shows how many calories are in different amounts of popcorn. which of these statements is true? there are 125 calories in 2 cups of popcorn. there are 50 calories per cup of popcorn. the unit rate of calories in popcorn is 73.5 calories per cup. there are 1.5 calories in 75 cups of popcorn.

Explanation:

Step1: Find the unit rate (calories per cup)

The graph has a point \((1.5, 75)\), which means 1.5 cups of popcorn have 75 calories. To find the unit rate (calories per cup), we use the formula for slope (since it's a proportional relationship, the slope is the unit rate): \( \text{Unit Rate} = \frac{\text{Calories}}{\text{Cups}} = \frac{75}{1.5} \)
\( \frac{75}{1.5} = 50 \), so the unit rate is 50 calories per cup.

Step2: Analyze each statement

• Statement 1: There are 125 calories in 2 cups of popcorn.

Using the unit rate (50 calories per cup), for 2 cups: \( 50 \times 2 = 100 \) calories, not 125. So this is false.

• Statement 2: There are 50 calories per cup of popcorn.

From Step 1, we found the unit rate is 50 calories per cup. This matches, so this is true.

• Statement 3: The unit rate of calories in popcorn is 73.5 calories per cup.

We calculated the unit rate as 50, not 73.5. False.

• Statement 4: There are 1.5 calories in 75 cups of popcorn.

The point \((1.5, 75)\) means 1.5 cups have 75 calories, not 75 cups having 1.5 calories. False.

Answer:

The true statement is: There are 50 calories per cup of popcorn.