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12 Nov 2024, 03:10
Kudos
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In 1999, nearly all households in Country X purchased salty snacks. About 91% of households bought potato chips, purchasing an average of 9.8 pounds and spending roughly $26 over the year. A broader category—all chips (including potato, corn, and tortilla)—was purchased by 95.5% of households, with average annual purchases of 16.3 pounds. Other salty snacks, such as pretzels, cheese puffs, microwave popcorn, and packaged or bulk nuts, were purchased by 96.8% of households.
Considering all salty snacks, 99.2% of households made purchases in 1999. Among those who did, the average household bought 31.8 pounds and spent approximately $76.40. On a per-person basis, the average quantity purchased was 14.5 pounds.
Three key points emerge:
• Salty snack consumption was nearly universal, so almost all households would have been affected by a per-pound tax.
• Purchase quantities and spending varied systematically by household characteristics and demographics.
• Despite this variation, salty snacks represented a relatively small portion of household spending.
Considering all salty snacks, 99.2% of households made purchases in 1999. Among those who did, the average household bought 31.8 pounds and spent approximately $76.40. On a per-person basis, the average quantity purchased was 14.5 pounds.
Three key points emerge:
• Salty snack consumption was nearly universal, so almost all households would have been affected by a per-pound tax.
• Purchase quantities and spending varied systematically by household characteristics and demographics.
• Despite this variation, salty snacks represented a relatively small portion of household spending.
In Country X, where there are 50 million households, the government is evaluating a per-pound tax on all salty snacks. Based on the information provided, and assuming that the quantity of salty snacks purchased remains unchanged, select Fewer if the total revenue generated by the listed tax rate would be expected to be less than $600 million. Otherwise, select More.
| Fewer | More | |
| 30 cents per pound | ||
| 35 cents per pound | ||
| 45 cents per pound |
ShowHide Answer
Official Answer
30 cents per pound: Fewer
35 cents per pound: Fewer
45 cents per pound: More
18 Nov 2024, 12:16
Kudos
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Official Solution:
We are given tax rates per pound, so each rate should be applied directly to the total pounds of salty snacks purchased.
According to the data, 99.2% of households in Country X purchased salty snacks. For estimation, we can round this to 100%, meaning all 50 million households are included. Each household purchased an average of 31.81 pounds, which we can reasonably approximate to 30 pounds for easier calculation. This gives a total of about 1.5 billion pounds of salty snacks purchased.
Start with the middle tax rate. At 35 cents per pound, the estimated revenue would be 1.5 billion × 0.35, which equals $525 million. This is clearly less than $600 million.
Since 25 cents per pound is lower, it would also generate less than $600 million, and no further calculation is necessary.
The 45-cent rate is more than 20 percent higher than 35 cents, so it would generate over 20 percent more than $525 million—easily exceeding $600 million.
Correct answer:
30 cents per pound "Fewer"
35 cents per pound "Fewer"
45 cents per pound "More"
Bunuel
We are given tax rates per pound, so each rate should be applied directly to the total pounds of salty snacks purchased.
According to the data, 99.2% of households in Country X purchased salty snacks. For estimation, we can round this to 100%, meaning all 50 million households are included. Each household purchased an average of 31.81 pounds, which we can reasonably approximate to 30 pounds for easier calculation. This gives a total of about 1.5 billion pounds of salty snacks purchased.
Start with the middle tax rate. At 35 cents per pound, the estimated revenue would be 1.5 billion × 0.35, which equals $525 million. This is clearly less than $600 million.
Since 25 cents per pound is lower, it would also generate less than $600 million, and no further calculation is necessary.
The 45-cent rate is more than 20 percent higher than 35 cents, so it would generate over 20 percent more than $525 million—easily exceeding $600 million.
Correct answer:
30 cents per pound "Fewer"
35 cents per pound "Fewer"
45 cents per pound "More"
