Two Part-Time Jobs and the 30-Hour Cap
Maya is planning her work schedule for the week. She can work at most 30 hours total. The café where she works pays $14.25 per hour but will schedule her for no more than 18 hours. The bookstore pays $11.50 per hour with no hour cap. Maya already has 12 café hours scheduled, and she spends a fixed $15 per week on bus fare for work. She wants her weekly take-home pay after bus fare to be at least $390. Let $b$ be the number of bookstore hours she works. Maya needs to know whether her target is reachable under the hour limits and what wage change would make it reachable.
1. Write an inequality in $b$ for the bookstore hours needed to reach $390 after bus fare, assuming she keeps the 12 café hours. Solve it and interpret the result.
Read the worked answer
Café pay for 12 hours is $12(14.25) = 171$ dollars. After bus fare, the inequality is
$171 + 11.50b - 15 \ge 390$.
Simplify:
$156 + 11.50b \ge 390$
$11.50b \ge 234$
$b \ge 20.3478$.
Since hours are usually scheduled in whole or half hours, she needs at least about 20.35 bookstore hours, or 21 whole hours, to reach $390. But 12 café hours plus 21 bookstore hours is 33 hours, which exceeds her 30-hour cap.
2. Can Maya meet both the $390 goal and the 30-hour cap? Determine the maximum take-home pay possible under the 30-hour cap and the café's 18-hour cap, and state whether the goal is feasible.
Read the worked answer
To maximize pay, Maya should use as many café hours as possible because the café pays more. She can work 18 café hours, leaving $30 - 18 = 12$ bookstore hours.
Maximum take-home pay:
$18(14.25) + 12(11.50) - 15 = 256.50 + 138 - 15 = 379.50$.
This is $390 - 379.50 = 10.50$ short of her goal. Under the 30-hour cap and the café's 18-hour cap, the $390 goal is not feasible.
3. Maya could ask the bookstore for a higher wage. What minimum bookstore hourly wage would make the $390 goal achievable while respecting both hour caps? Assume she still works 18 café hours and 12 bookstore hours.
Read the worked answer
Let $w$ be the bookstore wage. With 18 café hours and 12 bookstore hours:
$18(14.25) + 12w - 15 \ge 390$
$256.50 + 12w - 15 \ge 390$
$241.50 + 12w \ge 390$
$12w \ge 148.50$
$w \ge 12.375$.
She would need at least $12.38 per hour at the bookstore, rounded up to the nearest cent. Check: $12.37$ gives $241.50 + 148.44 = 389.94$, which is still short; $12.38$ gives $241.50 + 148.56 = 390.06$, which meets the goal.