Difference between revisions of "1999 AMC 8 Problems/Problem 9"
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− | + | ==problem== | |
+ | |||
+ | Three fower 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 | ||
+ | (A) 850 (B) 1000 (C) 1150 (D) 1300 | ||
+ | (E) 1450 | ||
+ | |||
+ | ==solution== | ||
+ | |||
+ | (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 = 1150 plants. | ||
+ | OR | ||
+ | Plants shared by two beds have been counted | ||
+ | twice, so the total is 500 + 450 + 350 ¡ 50 ¡ 100 = | ||
+ | 1150 . | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC8 box|year=1999|num-b=8|num-a=10}} |
Revision as of 15:02, 4 November 2012
problem
Three fower 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 (A) 850 (B) 1000 (C) 1150 (D) 1300 (E) 1450
solution
(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 = 1150 plants. OR Plants shared by two beds have been counted twice, so the total is 500 + 450 + 350 ¡ 50 ¡ 100 = 1150 .
See Also
1999 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |