Question

11 a store sold plates for $5 each and mugs for $3 each.
nathan wrote the equation \\(5p + 3m = 75\\) to calculate the number of plates and mugs he could buy for exactly $75.
how many plates and mugs did nathan buy for $75?

• 5 plates and 3 mugs
• 5 plates and 12 mugs
• 9 plates and 10 mugs
• 15 plates and 25 mugs

12 leo recorded the number of pages he printed over five weeks.
17, 22, 17, 24, 20
what is the mean number of pages leo printed?

13 a jam recipe uses 2 cups of sugar for every 3 cups of fruit.
select the correct combination of sugar and fruit for this recipe.

• \\(\frac{1}{2}\\) cup of sugar, \\(\frac{1}{3}\\) cup of fruit
• 1 cup of sugar, 1.5 cups of fruit
• 1.5 cups of sugar, 2.5 cups of fruit
• 4 cups of sugar, 5 cups of fruit

14 a class is making crystals using sugar-water and string.
each student needs 0.25 litres of sugar-water for the experiment.
how many millilitres of sugar-water does each student need?
millilitres

Explanation:

Solve Question 11

Using the Algebraic Modeling knowledge point, we test which given option \((p, m)\) satisfies the linear equation:

$$5p + 3m = 75$$

• Option 1: \(5(5) + 3(3) = 25 + 9 = 34

eq 75\)

• Option 2: \(5(5) + 3(12) = 25 + 36 = 61

eq 75\)

• Option 3: \(5(9) + 3(10) = 45 + 30 = 75\) (Correct)
• Option 4: \(5(15) + 3(25) = 75 + 75 = 150

eq 75\)

Solve Question 12

To find the mean number of pages Leo printed, we sum the values and divide by the total count of weeks:

$$\text{Sum} = 17 + 22 + 17 + 24 + 20 = 100$$

$$\text{Mean} = \frac{100}{5} = 20$$

Solve Question 13

Using the Proportional Reasoning knowledge point, the ratio of sugar to fruit is:

$$\frac{\text{sugar}}{\text{fruit}} = \frac{2}{3}$$

We check which option maintains this ratio:

• Option 1: \(\frac{1/2}{1/3} = \frac{3}{2}

eq \frac{2}{3}\)

• Option 2: \(\frac{1}{1.5} = \frac{1}{3/2} = \frac{2}{3}\) (Correct)
• Option 3: \(\frac{1.5}{2.5} = \frac{3}{5}

eq \frac{2}{3}\)

• Option 4: \(\frac{4}{5}

eq \frac{2}{3}\)

Solve Question 14

To convert litres to millilitres, we multiply the volume by the conversion factor \(1000\text{ mL/L}\):

$$0.25\text{ L} \times 1000\text{ mL/L} = 250\text{ mL}$$

Answer:

Question 11

• (A) 5 plates and 3 mugs
• (B) 5 plates and 12 mugs
• (C) 9 plates and 10 mugs (Correct answer)
• (D) 15 plates and 25 mugs

Question 12

<blank>20</blank>

Question 13

• (A) \(\frac{1}{2}\) cup of sugar, \(\frac{1}{3}\) cup of fruit
• (B) 1 cup of sugar, 1.5 cups of fruit (Correct answer)
• (C) 1.5 cups of sugar, 2.5 cups of fruit
• (D) 4 cups of sugar, 5 cups of fruit

Question 14

A class is making crystals using sugar-water and string. Each student needs 0.25 litres of sugar-water for the experiment. How many millilitres of sugar-water does each student need? <blank>250</blank> millilitres