Sandwiches 8
(page 155)

Here's an exhaustive solution sent in by some North Carolinians:

(March 2004)

This is how my group solved Sandwiches 8:

1st-We read all of the clues and wrote them down:
1-350 Eighth graders
2-3/7 of Eighth graders bring lunch
3-20 More students bought sandwiches than brought.
4-31% of cafateria lunches featured sandwiches
5-72% of eighth graders who bring lunches have sandwiches in their lunches.
6-Less than half of students had sandwiches, but only by a few percent.

2nd-Using steps 1 and 2 ((above)), we multiplied 3/7 times 350, telling us that 150 eighth graders bring lunch.

3rd-Using the above number ((150)), and step 5, we multiplied it by 72%, which told us that 108 of the 150 students that bring lunches, have sandwiches.

4th-Using 150, and step 1, we subtracted 150 from 350, which showed that 200 eighth graders bought lunches.

5th-Using step 4, we found 31% of 200, which is 62, and shows that 62 of the 200 eighth graders that bought lunches, had sandwiches.

6th-Using the above answers, we added the 62 eighth graders that buy sandwiches and the 108 students that bring sandwiches, telling us that 170 of the 350 eighth graders, had sandwiches in their lunches last Wednesday.

7th-Then, we transformed that into a fraction, then being 170/350, which, in decimal form, is 0.485714285.

8th-Assuming that there are the same number of students in each of the three middle school grades, we multiplied 350 times 3. Which gave us 1050 students in the whole school.

9th-Then, using the decimal, 0.485714285, or 170/350, we multiplied that by
1050, which gave us 510 students, overall, that had sandwiches last Wednesday. 10th-To check our answer, we divided 1050 by 2, which gave us 525. The number had to be < Half of the students, so 510 worked.

Thank you,
Raleigh, North Carolina
Durant Road Middle School
7th Grade
Track 3
Mrs. Nelson's Compacted Math Class

eeps comments:

Hooray! The first solution for this problem! Thank you VERY much for explaining all the steps you used, adnm so clearly. Readers: do you agree? And what do you suppose "Compacted" means?? We hope it's not something that Mrs. Nelson does to her students when they misbehave...

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