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A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?
- a)20
- b)21
- c)22
- d)23
- e)24
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A basket of 1430 apples is divided equally among a group of apple love...
The best answer is C.
Try to back-solve the problem. (1430/22 = 65) people, if 45 came then there are 110 people.
(1430/110 = 13) apples, which is 9 apples less per person
(1430/110 = 13) apples, which is 9 apples less per person
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A basket of 1430 apples is divided equally among a group of apple love...
Let's solve the problem step by step:
Let the number of apples each person initially receives be x:
Given that a basket of 1430 apples is divided equally among a group of apple lovers, we have:
Number of people * Number of apples each person initially receives = Total number of apples
x * Number of people = 1430
x = 1430 / Number of people
When 45 people join the group:
Now, each person receives 9 apples less, so the new number of apples each person receives is x - 9.
The total number of apples remains the same:
Number of people * Number of apples each person receives = Total number of apples
(x - 9) * (Number of people + 45) = 1430
Substitute the value of x from the first equation:
(1430 / Number of people - 9) * (Number of people + 45) = 1430
1430 + 45*1430/Number of people - 9(Number of people + 45) = 1430
45*1430/Number of people - 9(Number of people + 45) = 0
45*1430 - 9(Number of people^2 + 45*Number of people) = 0
45*1430 = 9(Number of people^2 + 45*Number of people)
5*143 = Number of people^2 + 45*Number of people
715 = Number of people^2 + 45*Number of people
715 = Number of people(Number of people + 45)
715 = Number of people(Number of people + 45)
Now, find the factors of 715:
715 = 5*11*13
Therefore, Number of people = 13
Substitute this back into x = 1430 / Number of people:
x = 1430 / 13
x = 110
Therefore, each person initially received 110 apples before 45 people joined the feast.
Thus, the correct answer is option C) 22.
Let the number of apples each person initially receives be x:
Given that a basket of 1430 apples is divided equally among a group of apple lovers, we have:
Number of people * Number of apples each person initially receives = Total number of apples
x * Number of people = 1430
x = 1430 / Number of people
When 45 people join the group:
Now, each person receives 9 apples less, so the new number of apples each person receives is x - 9.
The total number of apples remains the same:
Number of people * Number of apples each person receives = Total number of apples
(x - 9) * (Number of people + 45) = 1430
Substitute the value of x from the first equation:
(1430 / Number of people - 9) * (Number of people + 45) = 1430
1430 + 45*1430/Number of people - 9(Number of people + 45) = 1430
45*1430/Number of people - 9(Number of people + 45) = 0
45*1430 - 9(Number of people^2 + 45*Number of people) = 0
45*1430 = 9(Number of people^2 + 45*Number of people)
5*143 = Number of people^2 + 45*Number of people
715 = Number of people^2 + 45*Number of people
715 = Number of people(Number of people + 45)
715 = Number of people(Number of people + 45)
Now, find the factors of 715:
715 = 5*11*13
Therefore, Number of people = 13
Substitute this back into x = 1430 / Number of people:
x = 1430 / 13
x = 110
Therefore, each person initially received 110 apples before 45 people joined the feast.
Thus, the correct answer is option C) 22.
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A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?a)20b)21c)22d)23e)24Correct answer is option 'C'. Can you explain this answer?
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