Sandwiches 7
(page 156)

Here's a solution sent in by Kathleen Sill, who appears to be from Wisconsin:

(March 2010)

Hi, I'm hoping this is the right place to send answers for United We Solve

There are 384 students in the 7th grade. Here is how this was solved

Bought Lunches = 5/8 of the students

Bought Lunches (with sandwiches) 40%
5/8 * 40% = 2/8 or 1/4 of the students

Bought Lunches (no sandwiches) = 60%
5/8 * 60% = 3/8

3/8 + 2/8 = 5/8 of the students that bought lunch

Brought Lunch from home 3/8 of the students bring lunch

2/3 of the students that bring lunch had a sandwich
2/3 * 3/8 = 6/24 = 1/4

Lunch from home (no sandwich)

1/3 * 3/8 = 3/24 = 1/8

1/4 + 1/8 = 3/8 of the students

Bought Lunch with sandwich plus brought sandwich from home

1/4 (bought) + 1/4 (home) = 192
1/2 of the students = 192
multiply both sides by 2
students = 384

1/4 of the students bought sandwiches (1/4 * 384) = 96 students
3/8 bought lunch no sandwich (384 * 3/8) = 144 students
1/4 of the students brought sandwiches (1/4 * 384) = 96 students
1/8 of the students brought lunch no sandwich (1/8 * 384) = 48 students

Twice as many seventh graders bought sandwiches in the cafeteria as brought lunches without sandwiches from home.

B = bought sandwiches
H = no sandwich from home
B = 2H
96 = 2 * 48 (48 is the number that brought lunch with no sandwich)

eeps comments:

Hooray! The first solution for this problem! So everyone, look at this and see, first, if you think it's right. Then think about how thoroughly explained it is. THEN think about how hard it is to describe solutions to problems like these even when you explain everything.

So what would make this easier to understand? I think there are two things (and no, I don't expect anyone to do all these things, I'm just using this hard work as an example):

One: make it clear which things are the answers

Two: maybe make a table or diagram to show results and even some of the logic

Finally, see how much she uses multiplication of fractions or percentages. If it's not obvious to you why this is important, you should hurry to figure it out!

 

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