what about this one On a voyage to Atlantis, Ariel from The Little Mermaid decided to pick up shells so that she could make necklaces for her mermaid friends. She picked up 30 green shells, 35 blue shells, and 30 yellow shells. 17 of the green shells had some blue in them. 15 of the shells had both yellow and blue in them, and 10 of the shells had both yellow and green in them. If just one shell had all three colors in it, how many total shells did Ariel pick up?

use Venn diagrams, fill in your data starting with the intersection of all three, then the intersection of two at a time, etc.

Please can you tell me the answer because I am very confused. Thanks

To find the total number of shells Ariel picked up, we need to add up the number of green, blue, and yellow shells. However, we need to be careful not to double-count the shells that have multiple colors.

Let's break down the information provided:

- Ariel picked up 30 green shells.
- Ariel picked up 35 blue shells.
- Ariel picked up 30 yellow shells.
- 17 green shells had blue in them.
- 15 shells had both yellow and blue in them.
- 10 shells had both yellow and green in them.
- Just one shell had all three colors.

To calculate the total number of shells, we will follow these steps:

Step 1: Add up the number of green, blue, and yellow shells without considering the overlapping colors.
30 green shells + 35 blue shells + 30 yellow shells = 95 shells (without considering overlaps)

Step 2: Subtract the shells with overlapping colors to avoid double-counting.
Subtract the number of shells with blue in them (17 shells) from the total count: 95 - 17 = 78 shells
Subtract the number of shells with both yellow and blue in them (15 shells): 78 - 15 = 63 shells
Subtract the number of shells with both yellow and green in them (10 shells): 63 - 10 = 53 shells

Step 3: Add the one shell that had all three colors.
53 shells + 1 shell = 54 shells

Therefore, Ariel picked up a total of 54 shells.