Question

ty received test grades of 83%, 74%, 79%, 79%, and 74%. (a) what grade would he need to make on the sixth test to get a c if a c is at least 75% but less than 80%? (b) is it possible for ty to get an a for his test average (at least 90%)? part 1 of 2 to earn a c in the course, ty must score at least 61% but less than 91% on the sixth test. part: 1 / 2 part 2 of 2 it is select for ty to get an a for his test average.

Explanation:

Part (a)

Step 1: Calculate sum of existing grades

Sum the given grades: \(83 + 74 + 79 + 79 + 74\)
\(83+74 = 157\), \(157+79 = 236\), \(236+79 = 315\), \(315+74 = 389\)

Step 2: Let \(x\) be the sixth grade, set up average inequality

Average of 6 tests: \(\frac{389 + x}{6}\)
For a C: \(75 \leq \frac{389 + x}{6} < 80\)

Step 3: Solve lower bound inequality

Multiply all parts by 6: \(75\times6 \leq 389 + x < 80\times6\)
\(450 \leq 389 + x < 480\)
Subtract 389: \(450 - 389 \leq x < 480 - 389\)
\(61 \leq x < 91\)

Part (b)

Step 1: Set up average inequality for A

For an A, average \(\geq 90\), so \(\frac{389 + x}{6} \geq 90\)

Step 2: Solve for \(x\)

Multiply both sides by 6: \(389 + x \geq 540\)
Subtract 389: \(x \geq 540 - 389 = 151\)
Since test grades max at 100%, \(x \geq 151\) is impossible.

Answer:

(a) At least \(61\%\) but less than \(91\%\)
(b) It is \(\boldsymbol{\text{impossible}}\) for Ty to get an A for his test average.