Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that the serving size of the cereal is 3/4 cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults.On Tuesday, Jennifer will mix Crunchy Grain cereal with Super Grain cereal for her breakfast. Super Grain cereal provides 240 calories per cup. If the total number of calories in one cup of Jennifer's mixture is 270, how much Super Grain cereal is in one cup of the mixture?
Correct answer: B. 1/4 cup
- A. 1/8 cup
- B. 1/4 cup
- C. 1/3 cup
- D. 1/2 cup
Explanation
Choice B is correct. It's given that a 3/4 cup serving of Crunch cereal provides 210 calories. The total number of calories per cup can be found by dividing 210 by 3/4, which gives 210 ÷ 3/4 = 280 calories per cup. Let c be the number of cups of Crunchy Grain cereal and s be the number of cups of Super Grain cereal. The expression 280c represents the number of calories in c cups of Crunchy Grain cereal, and 240s represents the number of calories in s cups of Super Grain cereal. The equation 280c + 240s = 270 gives the total number of calories in one cup of the mixture. Since c + s = 1 cup, c = 1 − s. Substituting 1 − s for c in the equation 280c + 240s = 270 yields 280(1 − s) + 240s = 270, or 280 − 280s + 240s = 270. Simplifying this equation yields 280 − 40s = 270. Subtracting 280 from both sides results in −40s = −10. Dividing both sides of the equation by −40 results in s = 1/4, so there is 1/4 cup of Super Grain cereal in one cup of the mixture.
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