# Math

Mary was making sandwiches for the class picnic. 13 of the sandwiches had a slice of cheese. 14 had a slice of salami. 13 had a slice of tomato. 8 had a slice of cheese & a slice of tomato. Only 3 had a just a slice of salami. 5 had a slice of tomato, a slice of cheese, & a slice of salami. 8 had a slice of tomato & a slice of salami. How many sandwiches did Mary make for the class picnic?

1. 👍 0
2. 👎 0
3. 👁 340
1. Using Venn diagram, start filling in the information

Put 5 in the intersection of all three
C+T --> 8, but we have already accounted for 5 of those, so put 3 into the intersection of only C and T
only S --> 3, so put 3 into S which is not part of any intersection
C+S --> 8 , but we have already accounted for 5 of those, so put 3 into the intersection of only C and S

the whole C circle is 13 , but 3+3+5 or 11 are already counted, so the only C part is 2
We don't know what only S and T is, call it x
For S, x+5+3+3=14
x = 3
For T, we already have 11, but the total of T is 13
so we would need 2 for "only T" part.

Complete C the same way, I get 2 for the "only C" part
Now add up all the components,
for a total of 21 sandwiches

1. 👍 0
2. 👎 1
2. How does this work though?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

Lisa needs to make 2 times as many tuna as cheese sandwiches and 4 times as many ham as cheese sandwiches. If Lisa makes 56 sandwiches, how many of each of the 3 kinds will she make?

2. ### math

A marketing firm wants to know how many people in District 6 have tried Popeyes' and Chick-fil-A's chicken sandwiches. Of the 10,000 people in District 6, 1500 are vegetarians or vegans and have never tried either sandwich, 5000

3. ### Math

Lisa needs to make 2 times as many tunas as cheese sandwiches and 4 times as many ham as cheese sandwiches. If Lisa makes 56 sandwiches, how many of each of the 3 kinds will she make?

4. ### algebra

the lappans buy three large sandwich wraps to serve at a picnic. Nine people in all will be at the picnic.Show three different ways to cut the sandwiches so that each person gets an equal share.

1. ### algebra 2

A cafeteria has 5 turkey sandwiches, 6 cheese sandwiches, and 4 tuna sandwiches. There are two students in line and each will take a sandwich. What isthe the probability that the first student takes a cheese sandwich and the next

2. ### algebra

Junior ate 30% of the sandwiches at the picnic. If he ate 1 Â˝ sandwiches, how many sandwiches were there? you cant solve this right? We can't?? Sez who? Let x denote the number of sandwiches. Then we're told 30%x=.30x=1.5

3. ### math

A group of friends decided to eat sandwiches. Their team leaders, Franco, Clint and Valir bought 46 sandwiches altogether for their organizationâ€™s getaway. Franco bought 5 more sandwiches than Valir. Meanwhile, Valir bought 8

4. ### math

Jason is trying to make picnic lunches.He has 12 sandwiches, 18 apples and 30 pieces of candy.How many lunches can he mmake if he wants each lunch to have the same number of each kind of food and use all of the food?

1. ### math

how many ways to divide 3 sandwiches for 9 people

2. ### Math

In health class, students recorded the weights of the sandwiches they have for lunch. The weights are shown in the line plot below. What is the average weight of one sandwich? X X X. X. X. X X. X. X. X 1/8. 1/4 3/8 1/2

3. ### math

At lunch, 8 friends share 6 sandwiches equally. What fraction of a sandwich does each friend get.

4. ### math

Joel made egg and tuna sandwiches in the ratio of 2:3. He then made 15 more tuna sandwiches and the ratio changed to 1:3. How many sandwiches did Joel make in all? 2/3=3/t; solving for t=4.5 when calculating to 15 tuna sandwiches,