Difference between revisions of "1999 AMC 8 Problems/Problem 9"
(Solution to 1998 AMC 8, #9) |
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− | + | ==Problem== | |
+ | |||
+ | 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 | ||
+ | |||
+ | <asy> | ||
+ | draw((0,0)--(3,0)--(3,1)--(0,1)--cycle); | ||
+ | draw(circle((.3,-.1),.7)); | ||
+ | draw(circle((2.8,-.2),.8)); | ||
+ | label("A",(1.3,.5),N); | ||
+ | label("B",(3.1,-.2),S); | ||
+ | label("C",(.6,-.2),S); | ||
+ | </asy> | ||
+ | |||
+ | <math>\text{(A)}\ 850 \qquad \text{(B)}\ 1000 \qquad \text{(C)}\ 1150 \qquad \text{(D)}\ 1300 \qquad \text{(E)}\ 1450</math> | ||
+ | |||
+ | ==Solution== | ||
+ | ===Solution 1=== | ||
+ | |||
+ | Plants shared by two beds have been counted | ||
+ | twice, so the total is <math>500 + 450 + 350 - 50 - 100 = \boxed{\text{(C)}\ 1150}</math>. | ||
+ | |||
+ | ===Solution 2=== | ||
+ | Bed A has <math>350</math> plants it doesn't | ||
+ | share with B or C. Bed B has <math>400</math> plants it doesn't | ||
+ | share with A or C. And C has <math>250</math> it doesn't share | ||
+ | with A or B. The total is <math>350 + 400 + 250 + 50 + | ||
+ | 100 = \boxed{\text{(C)}\ 1150}</math> plants. | ||
+ | |||
+ | ==Video Solution== | ||
+ | |||
+ | https://youtu.be/lajfUn8R6M4 ~DSA_Catachu | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC8 box|year=1999|num-b=8|num-a=10}} | ||
+ | {{MAA Notice}} |
Revision as of 12:26, 6 July 2020
Problem
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
Solution
Solution 1
Plants shared by two beds have been counted twice, so the total is .
Solution 2
Bed A has plants it doesn't share with B or C. Bed B has plants it doesn't share with A or C. And C has it doesn't share with A or B. The total is plants.
Video Solution
https://youtu.be/lajfUn8R6M4 ~DSA_Catachu
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.