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Marrrta [24]
2 years ago
10

A student scored 75 and 97 on her first two quizzes. Write and solve a compound inequality to find the possible values for a thi

rd quiz score that would give her an average between 85 and 90, inclusive.

Mathematics
1 answer:
Rainbow [258]2 years ago
3 0

Answer:

85 \le \frac{75 + 97 + n}{3} \le 90; 83 \le n \le 98

Step-by-step explanation:

Score of the first two quizzes: 75 and 97

Let n represent the third score

Average score would be: \frac{75 + 97 + n}{3}.

Given that the average score fall between 85 and 90, this can be represented by the compound inequality as shown below:

85 \le \frac{75 + 97 + n}{3} \le 90

Solve for n in each statement that makes up the compound inequality:

85 \le \frac{75 + 97 + n}{3}

85 \le \frac{172 + n}{3}

Multiply both sides by 3

85*3 \le 172 + n

255 \le 172 + n

Subtract 172 from each side of the inequality

255 - 172 \le n

83 \le n

Also,

\frac{75 + 97 + n}{3} \le 90

\frac{172 + n}{3} \le 90

Multiply both sides by 3

172 + n \le 90*3

172 + n \le 270

Subtract 172 from both sides of the inequality

n \le 270 - 172

n \le 98

Combining both together, the possible values of her third quiz score would be:

83 \le n \le 98

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