Question

1. the information for two pay - as - you - go cell phone companies is given.

on call: 3.5 hours: $10
talk time: $\frac{1}{2}$ hour: $1.25$
a. what is the unit rate in dollars per hour for each company?
on call; 2.86 per hour
talk time: 2.5 per hour
b. analyze relationships which company offers the best deal? explain your answer.
c. what if? another company offers a rate of $0.05 per minute. how would you find the unit rate per hour?
d. draw conclusions is the rate in part c a better deal than on call or talk time? explain.

1. represent real - world problems your teacher asks you to find a recipe that includes two ingredients with a rate of $\frac{2\text{ units}}{3\text{ units}}$.

a. give an example of two ingredients in a recipe that would meet this requirement.

Explanation:

Step1: Calculate unit - rate for On Call

To find the unit - rate for On Call, divide the total cost by the total number of hours. The cost is $10 for 3.5 hours. So the unit - rate $r_{1}=\frac{10}{3.5}\approx2.86$ dollars per hour.

Step2: Calculate unit - rate for Talk Time

For Talk Time, the cost is $1.25 for $\frac{1}{2}$ hour. To find the unit - rate, use the formula $r = \frac{C}{t}$, where $C$ is the cost and $t$ is the time. So $r_{2}=\frac{1.25}{\frac{1}{2}}=1.25\times2 = 2.5$ dollars per hour.

Step3: Analyze which company offers the best deal (Answer for part b)

The lower the unit - rate, the better the deal. Since $2.5<2.86$, Talk Time offers the best deal.

Step4: Calculate unit - rate for the new company (Answer for part c)

The new company offers a rate of $0.05$ per minute. Since there are 60 minutes in an hour, to find the unit - rate per hour, multiply the rate per minute by 60. So the unit - rate $r_{3}=0.05\times60 = 3$ dollars per hour.

Step5: Compare the new rate with previous rates (Answer for part d)

The unit - rate of On Call is approximately $2.86$ dollars per hour, the unit - rate of Talk Time is $2.5$ dollars per hour, and the unit - rate of the new company is $3$ dollars per hour. Since $2.5<2.86<3$, the rate in part c is not a better deal than On Call or Talk Time.

Answer:

a. On Call: approximately $2.86$ dollars per hour; Talk Time: $2.5$ dollars per hour
b. Talk Time offers the best deal because its unit - rate ($2.5$ dollars per hour) is lower than On Call's ($2.86$ dollars per hour).
c. Multiply the rate per minute ($0.05$) by 60. The unit - rate per hour is $3$ dollars per hour.
d. No. The rate of the new company ($3$ dollars per hour) is higher than the rates of On Call ($2.86$ dollars per hour) and Talk Time ($2.5$ dollars per hour).