Tom is on a certain diet that requires him to limit the

BTGmoderatorDC 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

OA A

Source: Manhattan Prep

For 10 days, Tom's total calory intake was 2,720*10 = 27,200 calories

Recommended calory intake for 10 days would be (2,400 + 200)*10 = 26,000 calories

Thus, extra intake = 27,200 – 26,000 = 1,200 calories

This extra 1,200 cal intake is because Tom splurged on a few days, taking 3 times the recommended the number of calories from snacks and dessert

Say Tom spurged for x days; thus, his extra intake of snacks and dessert per day = 3*200 – 200 = 400 cal; subtracted 200 since the recommended intake of 200 cal was already taken into the account in 26,000 cal.

=> 1,200 = 400x => x = 3 days

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorDC 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

OA A

Source: Manhattan Prep

We can let n = the number of days he splurges. Notice that on each of these n days, the total calorie intake 2400 + 3 x 200 = 3000. For each of the 10 - n days he doesn’t splurge, the total calorie intake is 2400 + 200 = 2600. Therefore, we can create the equation:

3000n + 2600(10 - n) = 2720 x 10

30n + 26(10 - n) = 272

30n + 260 - 26n = 272

4n = 12

n = 3

Answer: A

BTGmoderatorDC 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

OA A

Source: Manhattan Prep

Tom’s regular daily calorie intake is 2400 + 200 = 2600 calories. When he splurges, his daily calorie intake is 2400 + 3 x 200 = 3000 calories. If we let n = the number of days he splurges, we can create the equation:

3000n + 2600(10 - n) = 2720(10)

30n + 26(10 - n) = 272

30n + 260 - 26n = 272

4n = 12

n = 3

Answer: A