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11.07 Using rates

Lesson

We have seen how we can identify and compare rates to decide on the best value for money when comparing similar items or comparing the speed of different objects. As rates arise frequently in everyday life, there are many more practical uses for rates and calculations involving rates. 

For example, we can use a pay rate (dollars per hour) to calculate how much money is earned in a week; we can use the speed (km/h) to predict how long it would take to reach a given location; and we can use rates to calculate and compare the cost of different phone plans with differing charge rates for data ($/GB) and phone calls ($/min).

Let's look through some more examples to see rates in action in everyday life.

 

Worked example

If Steve earns $\$157.05$$157.05 for working $9$9 hours over the weekend and Tina earns $\$144.00$$144.00 for working $8$8 hours.

(a) Who has the better rate of pay?

Think: To work this out, we need a common point of comparison, let's work out how much each person earns per hour.

Do:

Steve: $\$157.05\div9$$157.05÷​9 hrs $=$= $\$17.45$$17.45/hr
       
Tina: $\$144.00\div8$$144.00÷​8 hrs $=$= $\$18.00$$18.00/hr

So now we can say with certainty that Tina's rate of pay is higher.

(b) How much will Tina earn in a week where she worked $35$35 hours at the same pay rate?

Think: She will receive $\$18$$18 for each hour she works. We need to multiply the pay rate by the number of hours.

Do:

Weekly pay $=$= $\$18\times35$$18×35
  $=$= $\$630$$630

 

(c) How many hours would it take to earn $\$1530$$1530?

Think: To find the number of hours we need to divide the total pay by the pay rate.

Do:

Hours worked $=$= $\frac{1530}{18}$153018
  $=$= $85$85 hours

 

Practice questions

Question 1

Christa earns $\$21$$21 per hour working as a receptionist. If she works $19$19 hours per week, how much is her weekly wage?

Question 2

Sally can vacuum $3$3 rugs in $15$15 minutes and squeeze $6$6 oranges in $24$24 minutes.

  1. How long does it take to vacuum $1$1 rug?

  2. How long does it take to squeeze $1$1 orange?

  3. How long would it take for Sally to vacuum $8$8 rugs and squeeze $12$12 oranges?

Question 3

Luke is a locksmith. On weekends, if he is on call, he gets paid $\$64.50$$64.50 per hour plus a flat rate call out fee of $\$75$$75.

On the coming Saturday he has $3$3 jobs that will take $1.5$1.5, $0.25$0.25 and $1.25$1.25 hours respectively to complete. How much will he earn on Saturday?

Question 4

Consider the following phone plans.

  1. Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Vodafone.

  2. Calculate the cost of a call with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Optus.

  3. Calculate the cost of a call (in dollars) with a duration of $6$6 minutes and $19$19 seconds on a $20 plan with Telstra.

  4. Calculate the cost of a call (in dollars) with a duration of $6$6 minutes and $19$19 seconds on a $19 plan with Virgin.

  5. Suppose the included value of each plan has been used up for the month. Which plan would then be the most cost-effective for calls with durations of $6$6 minutes and $19$19 seconds?

    Optus

    A

    Telstra

    B

    Virgin

    C

    Vodafone

    D

    Optus

    A

    Telstra

    B

    Virgin

    C

    Vodafone

    D

Outcomes

ACMEM073

complete calculations with rates, including solving problems involving direct proportion in terms of rate

ACMEM074

use rates to make comparisons

ACMEM075

use rates to determine costs; for example, calculating the cost of a tradesman using rates per hour, call-out fees

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