AMC8 1999

AMC8 1999 · Q9

AMC8 1999 · Q9. It mainly tests Inclusion–exclusion (basic).

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

三个花坛如图所示重叠。A 花坛有 500 株植物，B 花坛有 450 株，C 花坛有 350 株。A 和 B 共享 50 株植物，A 和 C 共享 100 株。总植物数是

(A) 850 850

(B) 1000 1000

(D) 1300 1300

(E) 1450 1450

Answer

Correct choice: (C)

正确答案：（C）

Solution

Plants shared by two beds have been counted twice, so the total is $500 + 450 + 350 - 50 - 100 = \boxed{\text{(C)}\ 1150}$. Bed A has $350$ plants it doesn't share with B or C. Bed B has $400$ plants it doesn't share with A or C. And C has $250$ it doesn't share with A or B. The total is $350 + 400 + 250 + 50 + 100 = \boxed{\text{(C)}\ 1150}$ plants.

两个花坛共享的植物被计数了两次，所以总计是 $500 + 450 + 350 - 50 - 100 = \boxed{\text{(C)}\ 1150}$。 A 花坛有 $350$ 株不与 B 或 C 共享的植物。B 有 $400$ 株不与 A 或 C 共享的。C 有 $250$ 株不与 A 或 B 共享的。总计是 $350 + 400 + 250 + 50 + 100 = \boxed{\text{(C)}\ 1150}$ 株植物。

Topics

CP.004 Inclusion–exclusion (basic)