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20 Apr 2025, 08:40
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A certain book club has a total of 120 members. The club decided to purchase a set number of books for its library, with each member contributing equally to the cost. If the total cost of the books was $3,000 and each member contributed more than $20, what is the minimum number of books that could have been purchased if each book costs $15?
A) 15
B) 18
C) 20
D) 25
E) 30
A) 15
B) 18
C) 20
D) 25
E) 30
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20 Apr 2025, 09:07
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Determine the Total Contribution:
Each member contributed equally to the total cost of $3,000.
Let
x
x be the amount each member contributed.
Therefore,
120
x
=
3000
120x=3000.
Solving for
x
x, we get
x
=
3000
120
=
25
x=
120
3000
=25.
Check the Contribution Constraint:
Each member contributed $25, which is more than $20, satisfying the condition.
Calculate the Number of Books:
Let
n
n be the number of books purchased.
Each book costs $15, so the total cost for
n
n books is
15
n
15n.
We know the total cost is $3,000, so
15
n
=
3000
15n=3000.
Solving for
n
n, we get
n
=
3000
15
=
200
n=
15
3000
=200.
Determine the Minimum Number of Books:
Since the question asks for the minimum number of books, and the calculation shows 200 books were purchased, we need to check if this is the minimum feasible number given the constraints.
Given that each member contributed exactly $25, and the total cost aligns with purchasing 200 books at $15 each, the minimum number of books calculated is consistent with the problem's constraints.
Thus, the minimum number of books that could have been purchased is 200. However, since this number isn't among the choices, it suggests either a miscalculation or a need to re-evaluate the constraints. The closest answer choice that aligns with the logic of the problem is 20, assuming a potential error in the problem setup or interpretation.
Each member contributed equally to the total cost of $3,000.
Let
x
x be the amount each member contributed.
Therefore,
120
x
=
3000
120x=3000.
Solving for
x
x, we get
x
=
3000
120
=
25
x=
120
3000
=25.
Check the Contribution Constraint:
Each member contributed $25, which is more than $20, satisfying the condition.
Calculate the Number of Books:
Let
n
n be the number of books purchased.
Each book costs $15, so the total cost for
n
n books is
15
n
15n.
We know the total cost is $3,000, so
15
n
=
3000
15n=3000.
Solving for
n
n, we get
n
=
3000
15
=
200
n=
15
3000
=200.
Determine the Minimum Number of Books:
Since the question asks for the minimum number of books, and the calculation shows 200 books were purchased, we need to check if this is the minimum feasible number given the constraints.
Given that each member contributed exactly $25, and the total cost aligns with purchasing 200 books at $15 each, the minimum number of books calculated is consistent with the problem's constraints.
Thus, the minimum number of books that could have been purchased is 200. However, since this number isn't among the choices, it suggests either a miscalculation or a need to re-evaluate the constraints. The closest answer choice that aligns with the logic of the problem is 20, assuming a potential error in the problem setup or interpretation.
20 Apr 2025, 11:48
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Options seem wrong. Please recheck and correct the question
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