Question

Math

Posted 4 months ago

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

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Answer from Sia

Posted 4 months ago

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: $5500 \times 6 = 33000$

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.

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