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 $\$ 50,000$.
$$
5500 P+4500 S \geq 50000
$$

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.

Question

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 $\$ 50,000$.
$$
5500 P+4500 S \geq 50000
$$

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.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Substitute the value of $P$ with 6 into the inequality $5500P + 4500S \geq 50000$. ‖ ‖ step 2 ⋮ Calculate the product of 5500 and 6: $5500 imes 6 = 33000$. ‖ ‖ step 3 ⋮ Rewrite the inequality with the calculated product: $33000 + 4500S \geq 50000$. ‖ ‖ step 4 ⋮ Subtract 33000 from both sides of the inequality to solve for $S$: $4500S \geq 50000 - 33000$. ‖ ‖ step 5 ⋮ Calculate the difference on the right side of the inequality: $50000 - 33000 = 17000$. ‖ ‖ step 6 ⋮ Divide both sides of the inequality by 4500 to isolate $S$: $S \geq \frac{17000}{4500}$. ‖ ‖ step 7 ⋮ Simplify the fraction to find the minimum value of $S$: $S \geq \frac{34}{9}$. ‖ ‖ step 8 ⋮ Since $S$ must be a whole number of months, round up $\frac{34}{9}$ to the next whole number, which is 4. ‖ ∻Answer∻ ⚹ Huang Yi must work as a sculptor for at least 4 months. ⚹ ∻Key Concept∻ ⚹Solving inequalities with a single variable⚹ ∻Explanation∻ ⚹To find the minimum number of months Huang Yi must work as a sculptor, we substitute the known value for $P$ into the inequality, simplify, and solve for $S$. Since $S$ represents whole months, we round up to the nearest whole number.⚹◊What is the minimum number of months she needs to work as a sculptor to reach her goal of making at least $50,000 given that she already worked 6 months as a paleontologist?⍭ Generate me a similar question◊$

Sia