Question

1. wayne and steve work at a photocopy shop. they have an order to print and bind 500 copies of a business report. steve finished 125 reports in 8.5 h and wayne finished the remaining 375 reports in 22 h. who worked at a faster rate? (2 marks)
2. on wednesday a crew paved 12 km of road in 7 h. on thursday, the crew paved 8 km in 6 h. draw a graph to compare the crew’s daily paving rates. (2 marks)
3. jamia is deciding between two long - distance telephone plans:

• plan a charges $5 per month plus 6¢/min.
• plan b charges $20 per month plus 1¢/min.

jamia usually makes about 200 min of long - distance calls each month. which plan costs less? show your calculations. (2 marks)

1. orange juice is sold in 2 l cartons and 350 ml boxes. a 2 l carton sells for $3.99 and six 350 ml boxes sell for $4.99. which size has the lower cost per millilitre? show your calculations. (2 marks)

Explanation:

Question 17

Step1: Calculate Steve's rate

$\text{Steve's rate} = \frac{125}{8.5} \approx 14.71 \text{ reports/h}$

Step2: Calculate Wayne's rate

$\text{Wayne's rate} = \frac{375}{22} \approx 17.05 \text{ reports/h}$

Step3: Compare the two rates

$17.05 > 14.71$

Step1: Calculate Wednesday's paving rate

$\text{Wednesday rate} = \frac{12}{7} \approx 1.71 \text{ km/h}$

Step2: Calculate Thursday's paving rate

$\text{Thursday rate} = \frac{8}{6} \approx 1.33 \text{ km/h}$

Step3: Summarize for graphing

To compare, plot the two rates on a bar graph:

• X-axis: Days (Wednesday, Thursday)
• Y-axis: Paving Rate (km/h)
• Bar 1 (Wednesday): ~1.71 km/h
• Bar 2 (Thursday): ~1.33 km/h

Step1: Calculate cost for Plan A

First, convert 200 min cost: $200 \times 0.06 = 12$
Total cost: $5 + 12 = 17$

Step2: Calculate cost for Plan B

First, convert 200 min cost: $200 \times 0.01 = 2$
Total cost: $20 + 2 = 22$

Step3: Compare the two costs

$17 < 22$

Answer:

Wayne worked at a faster rate.

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Question 18