Problem Solving

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


Am I solving this correctly? I haven't seen this approach online.


10(days)*2,720(ave per day)=27,200

2400(10 days)+200X=27,200

24,000+200X=27,200

200X=3200

X=16

16 (total snacks) -10 (total days) = 6 (extra snacks consumed)

6/2(he takes 3 times the recommended calories, I already included 1 time in the above equation, therefore I divide by 2) = 3

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

This is a weighted average/mixture question.

Ingredient 1: Average caloric intake on deprived days = meal calories + snack calories = 2400 + 200 = 2600.
Ingredient 2: Average caloric intake on splurge days = meal calories + snack calories = 2400 + 3*200 = 3000.
Mixture: Average caloric intake for the MIXTURE of deprived days and splurge days = 2720.

Let D = the number of deprived days and S = the number of splurge days.
To determine the ratio of D to S in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the average for the mixture in the middle.
D 2600--------------2720-------------3000 S

Step 2: Calculate the distances between the averages.
D 2600------120----2720-----280-----3000 S

Step 3: Determine the ratio in the mixture.
The required ratio of D to S is the RECIPROCAL of the distances in red.
D:S = 280:120 = 7:3.

Thus, of the 10 days, D=7 and S=3.

The correct answer is A.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

GMATGuruNY 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

This is a weighted average/mixture question.

Ingredient 1: Average caloric intake on deprived days = meal calories + snack calories = 2400 + 200 = 2600.
Ingredient 2: Average caloric intake on splurge days = meal calories + snack calories = 2400 + 3*200 = 3000.
Mixture: Average caloric intake for the MIXTURE of deprived days and splurge days = 2720.

Let D = the number of deprived days and S = the number of splurge days.
To determine the ratio of D to S in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the average for the mixture in the middle.
D 2600--------------2720-------------3000 S

Step 2: Calculate the distances between the averages.
D 2600------120----2720-----280-----3000 S

Step 3: Determine the ratio in the mixture.
The required ratio of D to S is the RECIPROCAL of the distances in red.
D:S = 280:120 = 7:3.

Thus, of the 10 days, D=7 and S=3.

The correct answer is A.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

That's an interesting approach. Thanks for the problem suggestion.