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10 Mar 2025, 21:49
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Number of 15-gallon drums: 15,000
Number of 25-gallon drums: 11,000
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (02:44) correct
26%
(03:14)
wrong
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A paint manufacturer has the option to ship its wholesale supply in either 15-gallon or 25-gallon drums. If the manufacturer is to ship exactly 500,000 gallons, and can order no more than 15,000 and no fewer than 10,000 drums of each type, which of the following combinations is a possible way for it to ship its paint?
| Number of 15-gallon drums | Number of 25-gallon drums | |
| 10,000 | ||
| 11,000 | ||
| 12,000 | ||
| 13,000 | ||
| 15,000 | ||
| 17,000 |
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Official Answer
Number of 15-gallon drums: 15,000
Number of 25-gallon drums: 11,000
poojaarora1818
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10 Mar 2025, 23:09
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Bismuth83
A paint manufacturer has the option to ship its wholesale supply in either 15-gallon or 25-gallon drums. If the manufacturer is to ship exactly 500,000 gallons, and can order no more than 15,000 and no fewer than 10,000 drums of each type, which of the following combinations is a possible way for it to ship its paint?
Solution : We look for the option values for 15-gallon (X) and 25-gallon (Y) and the total should come down to 500,000
Let's follow the equation 15x + 25Y = 500,000
The only value that fits for the value of X is 15000 and Y is 11000.
So, 15 gallons is 15000 and 25 gallons is 11000.
10 Mar 2025, 23:41
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To solve this, we need to calculate the number of gallons shipped based on each combination of 15-gallon and 25-gallon drums. The total number of gallons shipped should equal 500,000, and the number of drums of each type should be between 10,000 and 15,000. Let’s go step by step:
Step 1: Formulate the equation
Let x be the number of 15-gallon drums and y be the number of 25-gallon drums. Then:
15x + 25y = 500,000
Step 2: Simplify the equation
Divide through by 5:
3x + 5y = 100,000
Step 3: Solve for valid combinations
We now test the given values of x(number of 15-gallon drums) to find y(number of 25-gallon drums) and ensure both x and y fall within the limits of 10,000 to 15,000 drums.
1. If x = 10,000:
3(10,000) + 5y = 100,000 \(\implies\) 30,000 + 5y = 100,000 \(\implies\) 5y = 70,000 \(\implies\) y = 14,000
y = 14,000 \) is valid.
2. If x = 11,000:
3(11,000) + 5y = 100,000 \(\implies\) 33,000 + 5y = 100,000 \(\implies\) 5y = 67,000 \(\implies\) y = 13,400
y = 13,400 is valid.
3. If x = 12,000:
3(12,000) + 5y = 100,000 \(\implies\) 36,000 + 5y = 100,000 \(\implies\) 5y = 64,000 \(\implies\) y = 12,800
y = 12,800 is valid.
4. If x = 13,000:
3(13,000) + 5y = 100,000 \(\implies\) 39,000 + 5y = 100,000 \(\implies\) 5y = 61,000 \(\implies\) y = 12,200
y = 12,200 is valid.
5. If x = 15,000:
3(15,000) + 5y = 100,000 \(\implies\) 45,000 + 5y = 100,000 \(\implies\) 5y = 55,000 \(\implies\) y = 11,000
y = 11,000 is valid.
6. If x = 17,000:
3(17,000) + 5y = 100,000 \(\implies\) 51,000 + 5y = 100,000 \(\implies\) 5y = 49,000 \(\implies\) y = 9,800
y = 9,800 is not valid because y < 10,000.
Step 4: List valid combinations
The valid combinations are:
x = 10,000, y = 14,000
x = 11,000, y = 13,400
x = 12,000, y = 12,800
x = 13,000, y = 12,200
x = 15,000, y = 11,000
Final Answer:
One valid combination is 15,000 (15-gallon drums) and 11,000 (25-gallon drums). It satisfies both:
Step 1: Formulate the equation
Let x be the number of 15-gallon drums and y be the number of 25-gallon drums. Then:
15x + 25y = 500,000
Step 2: Simplify the equation
Divide through by 5:
3x + 5y = 100,000
Step 3: Solve for valid combinations
We now test the given values of x(number of 15-gallon drums) to find y(number of 25-gallon drums) and ensure both x and y fall within the limits of 10,000 to 15,000 drums.
1. If x = 10,000:
3(10,000) + 5y = 100,000 \(\implies\) 30,000 + 5y = 100,000 \(\implies\) 5y = 70,000 \(\implies\) y = 14,000
y = 14,000 \) is valid.
2. If x = 11,000:
3(11,000) + 5y = 100,000 \(\implies\) 33,000 + 5y = 100,000 \(\implies\) 5y = 67,000 \(\implies\) y = 13,400
y = 13,400 is valid.
3. If x = 12,000:
3(12,000) + 5y = 100,000 \(\implies\) 36,000 + 5y = 100,000 \(\implies\) 5y = 64,000 \(\implies\) y = 12,800
y = 12,800 is valid.
4. If x = 13,000:
3(13,000) + 5y = 100,000 \(\implies\) 39,000 + 5y = 100,000 \(\implies\) 5y = 61,000 \(\implies\) y = 12,200
y = 12,200 is valid.
5. If x = 15,000:
3(15,000) + 5y = 100,000 \(\implies\) 45,000 + 5y = 100,000 \(\implies\) 5y = 55,000 \(\implies\) y = 11,000
y = 11,000 is valid.
6. If x = 17,000:
3(17,000) + 5y = 100,000 \(\implies\) 51,000 + 5y = 100,000 \(\implies\) 5y = 49,000 \(\implies\) y = 9,800
y = 9,800 is not valid because y < 10,000.
Step 4: List valid combinations
The valid combinations are:
x = 10,000, y = 14,000
x = 11,000, y = 13,400
x = 12,000, y = 12,800
x = 13,000, y = 12,200
x = 15,000, y = 11,000
Final Answer:
One valid combination is 15,000 (15-gallon drums) and 11,000 (25-gallon drums). It satisfies both:
- 15(15,000) + 25(11,000) = 500,000
- The range for x (15-gallon drums) and y (25-gallon drums) is within 10,000–15,000
