Question

1. wireless earbuds are sold for $75 per pair. if a total of $1,521 in general expenses plus $25 per pair are spent manufacturing the earbuds, how many pairs must be sold to make at least $9,000 profit?
2. jenny has scores of 78, 89, 90, and 96 on her first four tests. out of 100 points, what score must she make on her next test in order to have at least an average of 90?

Explanation:

For Problem 8:

Step1: Define variables and profit formula

Let $x$ = number of earbud pairs. Profit = Revenue - Total Cost.
Revenue = $75x$, Total Cost = $1521 + 25x$.
Profit inequality: $75x - (1521 + 25x) \geq 9000$

Step2: Simplify the inequality

$75x - 1521 - 25x \geq 9000$
$50x - 1521 \geq 9000$

Step3: Isolate the term with $x$

$50x \geq 9000 + 1521$
$50x \geq 10521$

Step4: Solve for $x$

$x \geq \frac{10521}{50}$
$x \geq 210.42$
Since partial pairs can't be sold, round up to the next whole number.

Step1: Define variable and average formula

Let $x$ = next test score. Average = $\frac{\text{Sum of all scores}}{\text{Number of tests}}$.
Inequality: $\frac{78 + 89 + 90 + 96 + x}{5} \geq 90$

Step2: Calculate sum of known scores

$78 + 89 + 90 + 96 = 353$
Inequality becomes: $\frac{353 + x}{5} \geq 90$

Step3: Eliminate denominator

$353 + x \geq 90 \times 5$
$353 + x \geq 450$

Step4: Solve for $x$

$x \geq 450 - 353$
$x \geq 97$

Answer:

211 pairs

---

For Problem 10: