1999 AMC 8 Problem 9

Below is the professionally curated solution for Problem 9 of the 1999 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 8 solutions, or check the answer key.

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Concepts:inclusion-exclusion Venn Diagram

Difficulty rating: 1020

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

$850$

$1000$

$1150$

$1300$

$1450$

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.

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