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For a sales promotion, a dog food producer produces packages with 40 percent more dog food than the regular-size package and sells the larger package for the same price as the usual price of the regular-size package. Compared to the regular-size package at its usual price, approximately what percent less is the price per ounce of the larger package of dog food?
A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%
2024-01-27_13-51-20.png [ 64.37 KiB | Viewed 14539 times ]
A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%
Attachment:
2024-01-27_13-51-20.png [ 64.37 KiB | Viewed 14539 times ]
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25 Nov 2023, 11:07
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BhavyaKamana
Regular-size Package
Assume
- Quantity = 100 ounce
- Price = $100
- Price per ounce = \(\frac{100}{100}\) = $1 per ounce
Promotional Package
The promotional package has 40% more dog food.
- Quantity = 100*1.4 = 140 ounce
- Price = $100
- Price per ounce = \(\frac{100}{140}\) = $ \(\frac{5}{7}\) per ounce
Price Difference = \(1 - \frac{5}{7} = \frac{2}{7}\)
Required Percentage = \(\frac{\frac{2}{7}}{1}*100\) = \(\frac{2}{7}*100\)
If the denominator were 8,
Required Percentage =\(\frac{2}{8}*100 = 25\)%
Hence, our answer will be greater than 25% but close to it. From the available options, the closest value is 29%.
Option B
General Discussion
27 Jun 2024, 13:19
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For a sales promotion, a dog food producer produces packages with 40 percent more dog food than the regular-size package and sells the larger package for the same price as the usual price of the regular-size package. Compared to the regular-size package at its usual price, approximately what percent less is the price per ounce of the larger package of dog food?
Let the normal size in ounces be S and the normal price be P.
The price per ounce for the normal size is P/S.
The price per ounce of the larger size is P/1.4S.
So, the percentage difference is the following:
(P/1.4S - P/S)/(P/S)
Simplifying, we get the following:
1/1.4 - 1 = 10/14 - 14/14 = -4/14 = -2/7
1/7 is a little less than 15%. So, 2/7 is around 29%.
A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%
Correct answer: B
Let the normal size in ounces be S and the normal price be P.
The price per ounce for the normal size is P/S.
The price per ounce of the larger size is P/1.4S.
So, the percentage difference is the following:
(P/1.4S - P/S)/(P/S)
Simplifying, we get the following:
1/1.4 - 1 = 10/14 - 14/14 = -4/14 = -2/7
1/7 is a little less than 15%. So, 2/7 is around 29%.
A. 25%
B. 29%
C. 37.5%
D. 40%
E. 60%
Correct answer: B
