Question

samantha has a babysitting business. the table to the right shows how much she charges. last week, she sat for two infants and for two toddlers. use this information to answer the question.
number of kids per day per hour
one infant $10 $4
two infants $30 $12
one or two toddlers $20 $9
for any of the babysitting services listed in the table, how many hours can be purchased before it would be cheaper to pay for one day?
_______ hours
(type a whole number.)

Explanation:

Step1: Analyze one infant service

Let $h_1$ = hours for 1 infant. Set hourly cost = daily cost:
$4h_1 = 10$
$h_1 = \frac{10}{4} = 2.5$
Whole hours before cheaper: 2

Step2: Analyze two infants service

Let $h_2$ = hours for 2 infants. Set hourly cost = daily cost:
$12h_2 = 30$
$h_2 = \frac{30}{12} = 2.5$
Whole hours before cheaper: 2

Step3: Analyze toddler service

Let $h_3$ = hours for toddlers. Set hourly cost = daily cost:
$9h_3 = 20$
$h_3 = \frac{20}{9} \approx 2.22$
Whole hours before cheaper: 2

Step4: Find maximum shared whole hour

All services have 2 as the highest whole hour where hourly cost is cheaper than daily cost.

Answer:

2