Question

1. ty received quiz grades of 66%, 70%, and 91%.

a. what grade would he need to get on the fourth quiz to earn a b average, that is, at least 80%?
b. is it possible for ty to get an a average for his quizzes (at least 90%)?

Explanation:

Step1: Set up the average formula for part a

Let \(x\) be the fourth - quiz grade. The average formula is \(\frac{66 + 70+91 + x}{4}\geq80\).
First, simplify the numerator: \(66 + 70+91=227\). So the inequality becomes \(\frac{227 + x}{4}\geq80\).

Step2: Solve the inequality for part a

Multiply both sides of the inequality \(\frac{227 + x}{4}\geq80\) by \(4\): \(227 + x\geq320\).
Subtract \(227\) from both sides: \(x\geq320 - 227\). So \(x\geq93\).

Step3: Set up the average formula for part b

The average formula is \(\frac{66 + 70+91 + y}{4}\geq90\).
Simplify the numerator: \(66 + 70+91 = 227\). The inequality becomes \(\frac{227 + y}{4}\geq90\).

Step4: Solve the inequality for part b

Multiply both sides of the inequality \(\frac{227 + y}{4}\geq90\) by \(4\): \(227 + y\geq360\).
Subtract \(227\) from both sides: \(y\geq360 - 227\). So \(y\geq133\). But since the maximum grade is \(100\%\), \(y = 133\) is not possible.

Answer:

a. Ty needs to get at least \(93\%\) on the fourth quiz to earn a B average.
b. It is not possible for Ty to get an A average for his quizzes, because he would need a grade of \(133\%\) on the fourth quiz, which is not feasible (assuming a maximum grade of \(100\%\)).