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Solve Proportion Problem: Calculate Calories Burned in 40 Minutes
Mathematics
Grade 7 (Junior High School)
Question Content
Set up a proportion and solve the following: When Katie works out at the gym for 25 minutes, she usually burns 150 calories. How many calories is she expected to burn when she works out for 40 minutes? Options: 300 calories, 240 calories, 180 calories, 220 calories
Correct Answer
240 calories
Detailed Solution Steps
1
Step 1: Define the proportion. Let x be the number of calories burned in 40 minutes. Since the rate of calories burned per minute is constant, we set up the proportion: (Calories burned)/(Time spent) = (Calories burned)/(Time spent), so 150/25 = x/40.
2
Step 2: Simplify the left side of the proportion. 150 divided by 25 equals 6, so the equation becomes 6 = x/40.
3
Step 3: Solve for x. Multiply both sides of the equation by 40: x = 6 * 40 = 240.
Knowledge Points Involved
1
Proportional Relationships
A proportional relationship exists when two quantities have a constant ratio. In real-world scenarios like this, it means the rate (calories burned per minute) stays the same, so we can set up equivalent fractions to find unknown values.
2
Setting Up Proportions
To set up a proportion, match corresponding quantities from two related scenarios. Here, we pair calories burned with time spent for both the known and unknown cases, ensuring the units are consistent on both sides of the equal sign.
3
Solving One-Variable Equations
Once the proportion is set up, it simplifies to a one-variable linear equation. We use inverse operations (like multiplying both sides by the denominator of the unknown term) to isolate the variable and find its value.
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