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guddo
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At the opening of business yesterday, there were 10 cereal boxes weigh 29 Jan 2024, 11:11
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75% (hard)

Question Stats:

71% (02:46) correct 29% (02:56) wrong based on 498 sessions

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At the opening of business yesterday, there were 10 cereal boxes weighing 20 ounces each and 20 cereal boxes weighing 15 ounces each on a certain grocery store shelf. If 18 of the boxes on that shelf were sold yesterday and the total weight of the unsold boxes was 220 ounces, then the number of sold boxes weighing 15 ounces was

A. 2
B. 4
C. 8
D. 12
E. 16

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Bunuel
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At the opening of business yesterday, there were 10 cereal boxes weigh 29 Jan 2024, 11:14
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guddo
At the opening of business yesterday, there were 10 cereal boxes weighing 20 ounces each and 20 cereal boxes weighing 15 ounces each on a certain grocery store shelf. If 18 of the boxes on that shelf were sold yesterday and the total weight of the unsold boxes was 220 ounces, then the number of sold boxes weighing 15 ounces was

A. 2
B. 4
C. 8
D. 12
E. 16

Show Spoiler
Attachment:
2024-01-29_22-01-36.png

Initially, there were 10 + 20 = 30 boxes, weighing 10*20 + 20*15 = 500 ounces.

Since the total weight of the unsold boxes was 220 ounces, the total weight of the 18 sold boxes was 500 - 220 = 280 ounces.

Hence, assuming the number of sold boxes weighing 15 ounces was x, the number of sold boxes weighing 20 ounces would be 18 - x. Thus, we'd have:

    15x + 20(18 - x) = 280
    x = 16

Answer: E.
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At the opening of business yesterday, there were 10 cereal boxes weigh 29 Jan 2024, 23:41
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guddo
At the opening of business yesterday, there were 10 cereal boxes weighing 20 ounces each and 20 cereal boxes weighing 15 ounces each on a certain grocery store shelf. If 18 of the boxes on that shelf were sold yesterday and the total weight of the unsold boxes was 220 ounces, then the number of sold boxes weighing 15 ounces was

A. 2
B. 4
C. 8
D. 12
E. 16

Show Spoiler
Attachment:
2024-01-29_22-01-36.png

Number of boxes unsold = \(30 - 18 = 12\)

Assume

  • The number of cereal boxes weighing 20 ounces that were unsold = \(x\)
  • The number of cereal boxes weighing 15 ounces that were unsold = \(y\)

\(x + y = 12\) -- (1)

\(20x + 15y = 220\) -- (2)

Multiplying equation (1) by 20 and subtracting (2) from the result

\(20x + 20y = 240\)
\(-20x -15y = -220\)
---------------------------------------------
\(5y = 20\)
\(y = 4\)

Hence, 4 unsold boxes were weighing 15 ounces.

The number of sold boxes weighing 15 ounces = \(20 - 4 - 16\)

Option E
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At the opening of business yesterday, there were 10 cereal boxes weigh 24 Apr 2025, 08:26
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guddo
At the opening of business yesterday, there were 10 cereal boxes weighing 20 ounces each and 20 cereal boxes weighing 15 ounces each on a certain grocery store shelf. If 18 of the boxes on that shelf were sold yesterday and the total weight of the unsold boxes was 220 ounces, then the number of sold boxes weighing 15 ounces was

A. 2
B. 4
C. 8
D. 12
E. 16

Show Spoiler
Attachment:
2024-01-29_22-01-36.png

Responding to a pm: Yes, we can use weighted averages here.

18 boxes were sold so 12 were unsold. Their weight was 220 ounces. So average weight = 220/12 = 55/3
\(\\
\\
\frac{w1}{w2} = \frac{(20 - 55/3)}{(55/3 - 15)} = \frac{(60 - 55)}{(55 - 45)} = \frac{1}{2}\\
\)

So the 12 unsold boxes are in the ratio 1 : 2 i.e. 4 boxes of 15 ounces are unsold and 8 boxes of 20 ounces are unsold.

Then 20 - 4 = 16 boxes of 15 ounces are sold.

Answer (E)

Check here for weighted averages: https://anaprep.com/arithmetic-weighted-averages/
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