16.0 grams of a certain food contain 130 calories. How many grams of this food would you need in order to consume 2150 calories?
The correct answer and explanation is :
To solve this problem, we are given:
- 16.0 grams of food = 130 calories
- We want to find how many grams = 2150 calories
Step 1: Set up a proportion
Since the number of calories increases proportionally with the number of grams, we can use a proportion to solve for the unknown quantity of grams:
[
\frac{16 \text{ grams}}{130 \text{ calories}} = \frac{x \text{ grams}}{2150 \text{ calories}}
]
Step 2: Cross-multiply and solve for ( x )
[
16 \times 2150 = 130 \times x
]
[
34400 = 130x
]
[
x = \frac{34400}{130} = 264.6 \text{ grams (rounded to one decimal place)}
]
✅ Correct Answer: 264.6 grams
🔍 Explanation (Approx. 300 words):
This problem is a practical example of solving a proportional relationship between two quantities—in this case, grams of food and the corresponding calories.
We are told that 16 grams of a certain food contains 130 calories. This means that for every 16 grams you consume, you get 130 calories of energy. Since the relationship is directly proportional, if you consume more grams of this food, you will also consume more calories in the same ratio.
To find out how many grams provide 2150 calories, we use the proportion method. In proportions, two ratios are set equal to each other. The ratio of grams to calories in the first known situation is the same as the ratio in the unknown situation. We set up the proportion:
[
\frac{16}{130} = \frac{x}{2150}
]
This tells us that ( x ), the unknown number of grams, will give us 2150 calories if the food continues to provide calories at the same rate. Using cross-multiplication, we solve for ( x ), resulting in ( x = 264.6 ) grams.
This approach can be applied in real-life nutrition planning—especially useful for dietitians and health-conscious individuals tracking calorie intake. It helps ensure a person can meet a calorie target while managing portion sizes accurately.