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Tom is on a certain diet that requires him to limit the number of calo
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15 Sep 2021, 09:33
15 Sep 2021, 09:33
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Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
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Re: Tom is on a certain diet that requires him to limit the number of calo
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15 Sep 2021, 10:02
15 Sep 2021, 10:02
1
Carcass wrote:
Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he follows the calorie guidelines precisely. If his average calorie intake for a 10 day period was 2720, on how many days did he splurge?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
We can also apply the formula for weighted averages:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Given:
Regular days: 2600 calories
Splurge days: 3000 calories
Let R = number of days in which Tom ate the regular amount
Let S = number of days in which Tom splurged
Since there were 10 days altogether, we can write: R + S = 10
Next, from the above formula, we get: 2720 = (R/10)(2600) + (S/10)(3000)
Multiply both sides by 10 to get: 27200 = 2600R + 3000S
Divide both sides by 100 to get: 272 = 26R + 30S
Rewrite as: 26R + 30S = 272
We now have a system of two equations that we must solve for S:
R + S = 10
26R + 30S = 272
Take the top equation and multiply both sides by 26 to get:
26R + 26S = 260
26R + 30S = 272
Subtract the red equation from the blue equation to get: 4S = 12
Solve, S = 3
Answer: A
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Re: Tom is on a certain diet that requires him to limit the number of calo
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03 Oct 2023, 11:21
03 Oct 2023, 11:21
1
If Tom follows his guidelines he would end up consuming \(2600\) calories per day for \(10 \)days, giving us a total of \(26,000\) calories. But we are told that he consumed \(2,720\) calories on average through out the 10 days. From here we can understand that Tom splurged on extra \(1,200\) dollars\( (2,720*10 - 26000)\). When he splurges we know he intakes additional \(400\) calories. So that leves us with 3 days of splurge for Tom \((1,200/400)\).
