Question

Huang Yi works as a paleontologist and a sculptor. She earns \$5{,}500$5,500dollar sign, 5, comma, 500 per month as a paleontologist and \$4{,}500$4,500dollar sign, 4, comma, 500 per month as a sculptor. Huang Yi wants to make more than \$50{,}000$50,000dollar sign, 50, comma, 000 this year. In the inequality shown above, PPP represents the number of months Huang Yi can work as a paleontologist and SSS represents the number of months she can work as a sculptor to reach her goal. If Huang Yi worked for 666 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?

Answer 1

4 months

Explanation:

Let 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 she works for P months as an paleontologist, her income would be 5500P while if she works for S months as a sculptor her income would be 4500S.

Her total income = 5500P + 4500S

Since she wants to earn more than $50000, hence:

5500P + 4500S > 50000

Given she worked as a paleontologist for 6 months, therefore:

5500(6) + 4500S > 50000

33000 + 4500S > 50000

4500S > 50000 - 33000

4500S > 17000

S > 17000/4500

S > 3.78

S > 4

The minimum whole number of months that she must work as a sculptor to reach her goal is 4 months