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In a school, the number of students who play soccer is twice the numbe
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13 Jan 2024, 00:54
13 Jan 2024, 00:54
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In a school, the number of students who play soccer is twice the number of students who play basketball. The number of students who play both the sports is twice the number of students who play only basketball. If 5,000 students play both the sports, how many students play only soccer?
(A) 5,500
(B) 8,500
(C) 10,000
(D) 12,000
(E) 18,500
(A) 5,500
(B) 8,500
(C) 10,000
(D) 12,000
(E) 18,500
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Re: In a school, the number of students who play soccer is twice the numbe
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18 Jan 2024, 22:58
18 Jan 2024, 22:58
1
Attachment:
File comment: Venn Diagram of Students
nuri graphics 500x500 (3).png [ 26.08 KiB | Viewed 488 times ]
nuri graphics 500x500 (3).png [ 26.08 KiB | Viewed 488 times ]
Let a = # of students who play soccer only, c = # of students who play basketball only, and b = # of students who play both.
Since 5,000 play both sports, b = 5000.
Since "the number of students who play both the sports is twice the number of students who play only basketball",
5000 = 2 * c
c = 2500
The number of students who play soccer = a + b
The number of students who play basketball = c + b
Since "the number of students who play soccer is twice the number of students who play basketball",
a + b = 2(c + b)
a + 5000 = 2(2500 + 5000)
a = 10,000
General Discussion
Re: In a school, the number of students who play soccer is twice the numbe
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19 Jan 2024, 11:12
19 Jan 2024, 11:12
1
Expert Reply
This is a great explanation both visually and in logic
