Question

23 a school vegetable garden has:

• 4 lettuce plants
• 2 less capsicum plants than spinach plants
• 4 times as many spinach plants as lettuce plants
• 1 parsley plant, 1 sage plant and 1 basil plant and
• the number of spinach plants is a quarter of the number of tomato plants.

how many plants are growing in the school vegetable garden?

24 a shop sells four sizes of cans of red kidney beans.
can 1: $1.76, red kidney beans 400 g
can 2: $1.89, red kidney beans 420 g
can 3: $1.00, red kidney beans 125 g
can 4: $2.40, red kidney beans 500 g
which can of red kidney beans costs the least per gram?
can 1
can 2
can 3
can 4

25 the sum of the interior angles of a pentagon can be found by first dividing it into triangles from one vertex.
what is the sum of the interior angles of this pentagon?
degrees

Explanation:

Solve Question 23

We need to find the total number of plants in the school vegetable garden. Let's define variables for each plant type based on the given clues:

• Lettuce plants: \(L = 4\)
• Spinach plants: \(S = 4 \times L = 4 \times 4 = 16\)
• Capsicum plants: \(C = S - 2 = 16 - 2 = 14\)
• Tomato plants: We are told that the number of spinach plants is a quarter of the number of tomato plants, so \(S = \frac{1}{4} T\), which means \(T = 4 \times S = 4 \times 16 = 64\).
• Other plants: 1 parsley plant, 1 sage plant, 1 basil plant, which equals 3 plants.

Now, we sum all the plants:

$$ \text{Total} = L + S + C + T + 3 = 4 + 16 + 14 + 64 + 3 = 101 $$

Solve Question 24

We need to find which can of red kidney beans costs the least per gram using Unit Rate Problems:

• Can 1: \(400\text{ g}\) for \(\$1.76\).

$$ \text{Unit Price}_1 = \frac{1.76}{400} = \$0.0044\text{ per gram} $$

• Can 2: \(420\text{ g}\) for \(\$1.89\).

$$ \text{Unit Price}_2 = \frac{1.89}{420} = \$0.0045\text{ per gram} $$

• Can 3: \(125\text{ g}\) for \(\$1.00\).

$$ \text{Unit Price}_3 = \frac{1.00}{125} = \$0.0080\text{ per gram} $$

• Can 4: \(500\text{ g}\) for \(\$2.40\).

$$ \text{Unit Price}_4 = \frac{2.40}{500} = \$0.0048\text{ per gram} $$

Comparing the unit prices, Can 1 has the lowest cost per gram (\(\$0.0044\)).

Solve Question 25

We need to find the sum of the interior angles of a pentagon.
Using Geometric Formulas, the sum of the interior angles of an \(n\)-sided polygon is given by:

$$ \text{Sum} = (n - 2) \times 180^\circ $$

For a pentagon, \(n = 5\):

$$ \text{Sum} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ $$

This matches the visual aid showing the pentagon divided into 3 triangles from one vertex.

Answer:

Question 23

The number of plants growing in the school vegetable garden is <blank>101</blank>.

Question 24

• Can 1 (Correct answer)
• Can 2
• Can 3
• Can 4

Question 25

What is the sum of the interior angles of this pentagon? <blank>540</blank> degrees.