Question

section 2: rates, ratios & proportions (5 marks)

1. if 2.54 cm = 1 inch, how many cm are in 30 inches?
2. a plumber charges a $50 call - out fee plus $65/hour. write an equation for the total cost (c) for h hours.
3. rachel types 715 words in 6.5 minutes. how many words/minute does she type?
4. who types faster: rachel (from q8) or adam (240 words in 4 mins)?
5. what is the slope of the line for the plumbers charges?

section 3: number sense &

Explanation:

Step1: Convert inches to cm

Multiply 30 inches by conversion factor.
$30 \times 2.54 = 76.2$

Step2: Define total cost equation

Fixed fee + hourly rate × hours.
$C = 50 + 65h$

Step3: Calculate Rachel's typing speed

Divide total words by time.
$\frac{715}{6.5} = 110$

Step4: Calculate Adam's typing speed

Divide total words by his time.
$\frac{240}{4} = 60$

Step5: Compare typing speeds

Rachel's speed > Adam's speed.
$110 > 60$

Step6: Identify slope from cost equation

Slope = hourly rate in linear equation.
Slope = 65

Answer:

1. 76.2 cm
2. $C = 50 + 65h$
3. 110 words/minute
4. Rachel types faster
5. 65