Question

Three flower beds overlap as shown. Bed $A$ has $500$ plants, bed $B$ has $450$ plants, and bed $C$ has $350$ plants. Beds $A$ and $B$ share $50$ plants, while beds $A$ and $C$ share $100.$ The total number of plants is

$850$

$1000$

$1150$

$1300$

$1450$

Answer: C

Concepts:inclusion-exclusion Venn Diagram

Difficulty rating: 1020

Small Hint:

Add the three bed counts first

Big Hint:

Subtract the overlaps that were counted twice

Solution:

Note there are $50 + 100 = 150$ plants that are in two beds and there are no plants in all three beds.

The total number of plants is then $500 + 450 + 350 - 150 = 1150.$ We subtract to get rid of the plants that we counted twice.

Thus, C is the correct answer.

1999 AMC 8 Problem 9

Answer: C

Difficulty rating: 1020

Small Hint:

Big Hint:

Solution:

Problem 9 in Other Years