Answer: [tex]4\ months[/tex]
Step-by-step explanation:
Let be "P" the number of months Huang Yi must work as a paleontologist and "S" the number of months she must work as a sculptor to make at least $50,000
The inequality given in the exercise is:
[tex]5500P+4500S \geq 50000[/tex]
Knowing that this year she worked for 6 months as a paleontologist, we can identify that:
[tex]P=6[/tex]
So in order to calculate the minimum number of months that Huang Yi must work as a sculptor to reach her goal, we have to substitute that value of "P" into the inequality and then we must solve for "S".
Then, we get:
[tex]5500(6)+4500S \geq 50000\\\\33000+4500S \geq 50000\\\\4500S \geq 50000-33000\\\\4500S\geq 17000\\\\S\geq \frac{17000}{4500}\\\\S\geq 3.77[/tex]
Therefore, we can conclude that minimum whole number of months that she must work as a sculptor to reach her goal is:
[tex]4\ months[/tex]
