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Huang Yi works as a paleontologist and a sculptor. She earns $5,500$ per month as a paleontologist and $4,500$ per month as a sculptor. Huang Yi wants to make more than $50,000$ this year. In the given inequality, $P$ represents the number of months Huang Yi can work as a paleontologist and $S$ represents the number of months she can work as a sculptor to reach her goal. If Huang Yi worked for $6$ months as a paleontologist this year, what is the minimum whole number of months that she must work as a sculptor to reach her goal?

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One-step inequalities: word problems

Full solution

Q. Huang Yi works as a paleontologist and a sculptor. She earns

5,500

per month as a paleontologist and

4,500

per month as a sculptor. Huang Yi wants to make more than

50,000

this year. In the given inequality,

P

represents the number of months Huang Yi can work as a paleontologist and

S

represents the number of months she can work as a sculptor to reach her goal. If Huang Yi worked for

6

months as a paleontologist this year, what is the minimum whole number of months that she must work as a sculptor to reach her goal?

Calculate Total Earnings: $\newline$ Calculate the total earnings from working as a paleontologist for $6$ months. $\newline$ $5500 \times 6 = 33000$
Subtract from Goal: $\newline$ Subtract the earnings from the goal to find out how much more she needs to earn. $\newline$ $50000 - 33000 = 17000$
Calculate Months Needed: $\newline$ Calculate the number of months needed as a sculptor to earn the remaining amount. $\newline$ $\frac{17000}{4500} \approx 3.78$
Round Up to Whole Number: $\newline$ Since she needs to work whole months, round up to the next whole number. $\newline$ $3.78 \rightarrow 4$

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