Question

on two examinations, you have grades of 89 and 87. there is an optional final examination, which counts as one grade. you decide to take the final in order to get a course grade of a, meaning a final average of at least 90. a. what must you get on the final to earn an a in the course? b. by taking the final, if you do poorly, you might risk the b that you have in the course based on the first two exam grades. if your final average is less than 80, you will lose your b in the course. describe the grades on the final that will cause this to happen. a. you must get at least a . b. you will lose your grade if you get less than a .

Explanation:

Step1: Set up the average - grade formula for part a

Let the grade on the final be $x$. The average of the three grades (two previous grades and the final) is $\frac{89 + 87+x}{3}$. To get an A, the average must be at least 90. So we set up the inequality $\frac{89 + 87+x}{3}\geq90$.

Step2: Solve the inequality for part a

First, simplify the numerator: $89 + 87=176$. The inequality becomes $\frac{176 + x}{3}\geq90$. Multiply both sides by 3: $176+x\geq270$. Then subtract 176 from both sides: $x\geq270 - 176=94$.

Step3: Set up the average - grade formula for part b

To lose the B, the average $\frac{89 + 87+x}{3}<80$.

Step4: Solve the inequality for part b

Simplify the numerator: $89 + 87 = 176$. The inequality is $\frac{176+x}{3}<80$. Multiply both sides by 3: $176+x<240$. Subtract 176 from both sides: $x<240 - 176 = 64$.

Answer:

a. 94
b. 64