Question
Rosa has a company that makes chairs. If they sell chairs, they will be priced at (60-0.3n) dollars each, how many chairs must be sold to have a income of $1080? You must take into account that n≤40.
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Answer to a math question Rosa has a company that makes chairs. If they sell chairs, they will be priced at (60-0.3n) dollars each, how many chairs must be sold to have a income of $1080? You must take into account that n≤40.
Nash
4.987 Answers
Solution:
1. Given:
- Price per chair:(60 - 0.3n)
- Income:1080
2. Set up the equation for income:
n \times (60 - 0.3n) = 1080
3. Expand the equation:
60n - 0.3n^2 = 1080
4. Rearrange to form a quadratic equation:
-0.3n^2 + 60n - 1080 = 0
5. Multiply through by-10
3n^2 - 600n + 10800 = 0
6. Use the quadratic formulan = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} a = 3 b = -600 c = 10800
n = \frac{600 \pm \sqrt{(-600)^2 - 4 \cdot 3 \cdot 10800}}{2 \cdot 3}
n = \frac{600 \pm \sqrt{360000 - 129600}}{6}
n = \frac{600 \pm \sqrt{230400}}{6}
n = \frac{600 \pm 480}{6}
7. Solve forn
- First solution:n = \frac{600 + 480}{6} = \frac{1080}{6} = 180
- Second solution:n = \frac{600 - 480}{6} = \frac{120}{6} = 20
8. Considering the constraintn \leq 40 n = 20
Thus, Rosa needs to sell:
n = 20 1080
1. Given:
- Price per chair:
- Income:
2. Set up the equation for income:
3. Expand the equation:
4. Rearrange to form a quadratic equation:
5. Multiply through by
6. Use the quadratic formula
7. Solve for
- First solution:
- Second solution:
8. Considering the constraint
Thus, Rosa needs to sell:
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