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Word Problem - How many pieces of candy











































Solve for pieces of candy

Nine people have some candy.

The person with the most candy has nine prices.

At least one person has no candy.

The average number is four pieces of candy per person.

Four pieces of candy is the median.

More people have two pieces of candy than any other number.

How many pieces of candy does each person have?

Comments for Word Problem - How many pieces of candy

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Feb 10, 2013
Solve
by: Staff


Answer

Part I

C = total number of pieces of candy

N₁ = number of pieces of candy for person 1

N₂ = number of pieces of candy for person 2

N₃ = number of pieces of candy for person 3

N₄ = number of pieces of candy for person 4

N₅ = number of pieces of candy for person 5

N₆ = number of pieces of candy for person 6

N₇ = number of pieces of candy for person 7

N₈ = number of pieces of candy for person 8

N₉ = number of pieces of candy for person 9


C = N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

The average number is four pieces of candy per person.

4 = (N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉)/9

The total number of pieces of candy is 36 (4 × 9 = 36)

36 = (N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉)

Four pieces of candy is the median.

N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

N₁ + N₂ + N₃ + N₄ + 4 + N₆ + N₇ + N₈ + N₉ = 36


The person with the most candy has nine prices.

N₉ = 9

At least one person has no candy.

N₁ = 0

N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

0 + N₂ + N₃ + N₄ + 4 + N₆ + N₇ + N₈ + 9 = 36

More people have two pieces of candy than any other number.

Therefore, at least two of the following three people must have 2 pieces of candy: N₂, N₃,

N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

0 + N₂ + 2 + 2 + 4 + N₆ + N₇ + N₈ + 9 = 36

N₆, N₇, and N₈ must be 5,6,7; 5,6,8; 5,7,8 or 6,7,8

If these three numbers are 6,7, and 8, then the total number of pieces of candy will exceed 36


If these three numbers are 5,7, and 8, then the total number of pieces of candy will exceed 36

If these three numbers are 5,6, and 8, then the total number of pieces of candy does equal 36

If this is the case, then N₂ = 0.



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Feb 10, 2013
Solve
by: Staff

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Part II


This is a 1st possible solution:

N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

0 + 0 + 2 + 2 + 4 + 5 + 6 + 8 + 9 = 36

If N₆, N₇, and N₈ are equal to 5,6,7


N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

0 + N₂ + 2 + 2 + 4 + 5 + 6 + 7 + 9 = 36

Since the sum of 0 + 2 + 2 + 4 + 5 + 6 + 7 + 9 = 35, N₂ must = 1

N₁ + N₂ + N₃ + N₄ + N₅ + N₆ + N₇ + N₈ + N₉

0 + 1 + 2 + 2 + 4 + 5 + 6 + 7 + 9 = 36


The Final Solution #1 is:


N₁ = 0 pieces of candy
N₂ = 0 piece of candy
N₃ = 2 pieces of candy
N₄ = 2 pieces of candy
N₅ = 4 pieces of candy
N₆ = 5 pieces of candy
N₇ = 6 pieces of candy
N₈ = 8 pieces of candy
N₉ = 9 pieces of candy



The Final Solution #2 is:


N₁ = 0 pieces of candy
N₂ = 1 piece of candy
N₃ = 2 pieces of candy
N₄ = 2 pieces of candy
N₅ = 4 pieces of candy
N₆ = 5 pieces of candy
N₇ = 6 pieces of candy
N₈ = 7 pieces of candy
N₉ = 9 pieces of candy





Thanks for writing.

Staff
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