Question

Huang Yi works as a paleontologist and a sculptor. Let PPP represent the number of months Huang Yi must work as a paleontologist and SSS represent the number of months she must work as a sculptor to make at least \$50{,}000$50,000dollar sign, 50, comma, 000. 5500P+4500S \geq 500005500P+4500S≥500005500, P, plus, 4500, S, is greater than or equal to, 50000 Huang Yi worked for 666 months as a paleontologist this year. What is the minimum number of months that she must work as a sculptor to reach her goal?

Answer 1

Answer:  $4\ months$

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:

$5500P+4500S \geq 50000$

Knowing that this year she worked for 6 months as a paleontologist, we can identify that:

$P=6$

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:

$5500(6)+4500S \geq 50000\\\\33000+4500S \geq 50000\\\\4500S \geq 50000-33000\\\\4500S\geq 17000\\\\S\geq \frac{17000}{4500}\\\\S\geq 3.77$

Therefore, we can conclude that minimum whole number of months that she must work as a sculptor to reach her goal is:

$4\ months$