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15 Nov 2024, 16:21
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Number of patterned skirts: 200
Number of pairs of pants: 200
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (03:37) correct
49%
(03:48)
wrong
based on 226
sessions
History
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Plans for the fall production at a small clothing manufacturer include pants in solid colors and skirts in both solids and patterns. The necessary fabric in solid colors can be purchased for $28 per yard, and the patterned fabrics cost $32 per yard. Skirts require 3 yards of fabric, and pants 5 yards. Based on demand forecasts and profit margins, the company wants to make 50% more skirts than pants and wants to make half as many solid skirts as patterned skirts. The company spends a total of $55,600 for fabrics. At that level of spending, how many patterned skirts and how many pairs of pants can the company produce?
| Number of patterned skirts | Number of pairs of pants | |
| 100 | ||
| 150 | ||
| 200 | ||
| 225 | ||
| 300 | ||
| 450 |
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Official Answer
Number of patterned skirts: 200
Number of pairs of pants: 200
15 Nov 2024, 21:22
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From the question, it can be noted that
Let the no. of pants be x
Let the no. of skirts be 1.5x
No. of Patterned skirts + No. of Solid skirts = 1.5x
From the Question, No. of Solid Skirts = 0.5* No. of Patterned Skirts
No. of Patterned Skirts = x
No. of Solid Skirts = 0.5x
Therefore, x*5*28+0.5x*3*28+x*3*32 = 55600
278x = 55600
x = 200
No. of Patterned Skirts = 200
No. of Pants = 200
Let the no. of pants be x
Let the no. of skirts be 1.5x
No. of Patterned skirts + No. of Solid skirts = 1.5x
From the Question, No. of Solid Skirts = 0.5* No. of Patterned Skirts
No. of Patterned Skirts = x
No. of Solid Skirts = 0.5x
Therefore, x*5*28+0.5x*3*28+x*3*32 = 55600
278x = 55600
x = 200
No. of Patterned Skirts = 200
No. of Pants = 200
16 Nov 2024, 11:00
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1. The question asks us to find out how many patterned skirts and how many pairs of pants can the company produce.
2. Let there be x solid skirts.
3. "wants to make half as many solid skirts as patterned skirts." This means that there are 2x patterned skirts. In addition: "the company wants to make 50% more skirts than pants." So, there are \(\frac{2x + x}{100% + 50%} = \frac{3x}{1.5} = 2x\) pants.
4. "The company spends a total of $55,600 for fabrics." We can then write an equation that explains the price: \(56000 = x * 3 * 28 + 2x * 3 * 32 + 2x * 5 * 28 = 560x \rightarrow x = 100\).
5. Our question can be rephrased into finding 2x and 2x. This ends up being 200.
2. Let there be x solid skirts.
3. "wants to make half as many solid skirts as patterned skirts." This means that there are 2x patterned skirts. In addition: "the company wants to make 50% more skirts than pants." So, there are \(\frac{2x + x}{100% + 50%} = \frac{3x}{1.5} = 2x\) pants.
4. "The company spends a total of $55,600 for fabrics." We can then write an equation that explains the price: \(56000 = x * 3 * 28 + 2x * 3 * 32 + 2x * 5 * 28 = 560x \rightarrow x = 100\).
5. Our question can be rephrased into finding 2x and 2x. This ends up being 200.
