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Huang Yi works as a paleontologist and a sculptor. Let P represent the number of months Huang Yi must work as a paleontologist and S represent the number of months she must work as a sculptor to make at least $50,000. 5500 P+4500 S >= 50000 Huang Yi worked for 6 months as a paleontologist this year. What is the minimum number of months that she must work as a sculptor to reach her goal? Choose 1 answer: (A) Huang Yi must work as a sculptor for at least 3 months. B Huang Yi must work as a sculptor for at least 4 months. (C) Huang Yi must work as a sculptor for at least 5 months. D Huang Yi must work as a sculptor for at least 6 months.

Huang Yi works as a paleontologist and a sculptor.\newlineLet P P represent the number of months Huang Yi must work as a paleontologist and S S represent the number of months she must work as a sculptor to make at least $50,000 \$ 50,000 .\newline5500P+4500S≥50000 5500 P+4500 S \geq 50000 \newlineHuang Yi worked for 66 months as a paleontologist this year. What is the minimum number of months that she must work as a sculptor to reach her goal?\newlineChoose 11 answer:\newline(A) Huang Yi must work as a sculptor for at least 33 months.\newline(B) Huang Yi must work as a sculptor for at least 44 months.\newline(C) Huang Yi must work as a sculptor for at least 55 months.\newline(D) Huang Yi must work as a sculptor for at least 66 months.

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Q. Huang Yi works as a paleontologist and a sculptor.\newlineLet P P represent the number of months Huang Yi must work as a paleontologist and S S represent the number of months she must work as a sculptor to make at least $50,000 \$ 50,000 .\newline5500P+4500S≥50000 5500 P+4500 S \geq 50000 \newlineHuang Yi worked for 66 months as a paleontologist this year. What is the minimum number of months that she must work as a sculptor to reach her goal?\newlineChoose 11 answer:\newline(A) Huang Yi must work as a sculptor for at least 33 months.\newline(B) Huang Yi must work as a sculptor for at least 44 months.\newline(C) Huang Yi must work as a sculptor for at least 55 months.\newline(D) Huang Yi must work as a sculptor for at least 66 months.
  1. Calculate Huang Yi's income: Huang Yi's income from working as a paleontologist for 66 months can be calculated by multiplying her monthly income as a paleontologist by the number of months she worked.\newlineIncome from paleontology = 5500×P5500 \times P\newlineGiven P=6P = 6 months,\newlineIncome from paleontology = 5500×65500 \times 6
  2. Calculate actual income from paleontology: Now, calculate the actual income from paleontology for 66 months.\newlineIncome from paleontology = 5500×6=$(33000)5500 \times 6 = \$(33000)
  3. Calculate amount needed from sculpting: Subtract the income from paleontology from the total goal of $50,000\$50,000 to find out how much more money Huang Yi needs to make as a sculptor.\newlineAmount needed from sculpting = Total goal - Income from paleontology\newlineAmount needed from sculpting = $50,000−$33,000\$50,000 - \$33,000
  4. Calculate minimum number of months: Calculate the amount needed from sculpting.\newlineAmount needed from sculpting = $50,000−$33,000=$17,000\$50,000 - \$33,000 = \$17,000
  5. Determine Huang Yi's required months of work: Now, we need to find out the minimum number of months Huang Yi must work as a sculptor to make the remaining $17,000\$17,000. We can use the inequality 4500×S≥17,0004500 \times S \geq 17,000, where SS is the number of months she needs to work as a sculptor.
  6. Determine Huang Yi's required months of work: Now, we need to find out the minimum number of months Huang Yi must work as a sculptor to make the remaining $17,000\$17,000. We can use the inequality 4500⋅S≥17,0004500 \cdot S \geq 17,000, where SS is the number of months she needs to work as a sculptor.Divide both sides of the inequality by 45004500 to solve for SS.S≥17,0004500S \geq \frac{17,000}{4500}
  7. Determine Huang Yi's required months of work: Now, we need to find out the minimum number of months Huang Yi must work as a sculptor to make the remaining $17,000\$17,000. We can use the inequality 4500⋅S≥17,0004500 \cdot S \geq 17,000, where SS is the number of months she needs to work as a sculptor.Divide both sides of the inequality by 45004500 to solve for SS.
    S≥17,0004500S \geq \frac{17,000}{4500}Calculate the minimum number of months SS.
    S≥17,0004500S \geq \frac{17,000}{4500}
    S≥3.777...S \geq 3.777...
    Since Huang Yi cannot work a fraction of a month, we round up to the nearest whole month.
  8. Determine Huang Yi's required months of work: Now, we need to find out the minimum number of months Huang Yi must work as a sculptor to make the remaining $17,000\$17,000. We can use the inequality 4500⋅S≥17,0004500 \cdot S \geq 17,000, where SS is the number of months she needs to work as a sculptor.Divide both sides of the inequality by 45004500 to solve for SS.
    S≥17,0004500S \geq \frac{17,000}{4500}Calculate the minimum number of months SS.
    S≥17,0004500S \geq \frac{17,000}{4500}
    S≥3.777...S \geq 3.777...
    Since Huang Yi cannot work a fraction of a month, we round up to the nearest whole month.Huang Yi must work as a sculptor for at least 44 months to reach her goal, as working for only 33 months would not be sufficient.

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