j_shreyans 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
Alternate approach:
Tom is allowed to take in 2400 calories each day from three square meals, and 200 calories each day.
Thus, calories consumed on regular days = 2400 + 200 = 2600.
On splurge days, Tom takes in three times the recommended number of calories from snacks and dessert.
Thus, calories consumed on splurge days = 2400 + 3*200 = 3000.
We can PLUG IN THE ANSWERS, which represent the number of splurge days.
When the correct answer choice is plugged in, the average caloric intake over 10 days = 2720.
Since the average caloric intake (2720) is closer to the number of calories consumed on regular days (2600) than to the number of calories consumed on splurge days (3000), there must be MORE REGULAR DAYS THAN SPLURGE DAYS.
Thus, the number of regular days must be GREATER THAN 5, while the number of splurge days must be LESS THAN 5.
Eliminate C, D and E.
Answer choice B: 4 splurge days
Total calories consumed over 4 splurge days = 4*3000 = 12000.
Total calories consumed over 6 regular days = 6*2600 = 15600.
Average caloric intake over all 10 days = (12000 + 15600)/10 = 2760.
The average calories intake is too high.
Eliminate B.
The correct answer is
A.
Answer choice
A: 3 splurge days
Total calories consumed over 3 splurge days = 3*3000 = 9000.
Total calories consumed over 7 regular days = 7*2600 = 18200.
Average caloric intake over all 10 days = (9000 + 18200)/10 = 2720.
Success!
The correct answer is
A.
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