Kim is building a path around a garden at the back of a house, as shown. The path is 0.5 m wide. Find the area of the path. Kim is mixing some concrete for the path. The concrete mix is made up of crushed rock, sand and cement in the ratio of 4 : 2 : 1 by weight. Kim needs 2.1 tonnes of concrete mix in the correct ratio. Calculate how many 15 kg bags of cement Kim needs to buy.

SSCE HSC Mathematics Standard Annuities: Kim is building a path around a

Kim is building a path around a garden at the back of a house, as shown - HSC - SSCE Mathematics Standard - Question 26 - 2023 - Paper 1

Question 26

Kim is building a path around a garden at the back of a house, as shown. The path is 0.5 m wide. Find the area of the path. Kim is mixing some concrete for the pat... show full transcript

Worked Solution & Example Answer:Kim is building a path around a garden at the back of a house, as shown - HSC - SSCE Mathematics Standard - Question 26 - 2023 - Paper 1

Step 1

Find the area of the path.

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Answer

To find the area of the path, we first need to determine the dimensions of the overall area including the path.

The garden dimensions are 8 m in length and 3 m in width.

Including the path, the overall dimensions become:

Length: 8 m + 2(0.5 m) = 9 m
Width: 3 m + 2(0.5 m) = 4 m

Now, we calculate the area of the total rectangle (garden + path): $Area_{total} = Length \times Width = 9 m \times 4 m = 36 m^2$

Next, we calculate the area of just the garden: $Area_{garden} = Length_{garden} \times Width_{garden} = 8 m \times 3 m = 24 m^2$

Now we can find the area of the path: $Area_{path} = Area_{total} - Area_{garden} = 36 m^2 - 24 m^2 = 12 m^2$

Step 2

Calculate how many 15 kg bags of cement Kim needs to buy.

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Answer

The concrete mix ratio is given as crushed rock, sand, and cement in the proportion of 4 : 2 : 1. This means the total ratio parts sum is:

$4 + 2 + 1 = 7$

From the total of 7 parts, the amount of cement in the mixture is: $Amount_{cement} = \frac{1}{7} \times 2.1 \text{ tonnes} = 0.3 \text{ tonnes}$

To convert this to kilograms: $0.3 ext{ tonnes} = 300 ext{ kg}$

Now, to find out how many 15 kg bags are needed: $Number\_of\_bags = \frac{300 \text{ kg}}{15 \text{ kg/bag}} = 20 \text{ bags}$

Kim is building a path around a garden at the back of a house, as shown - HSC - SSCE Mathematics Standard - Question 26 - 2023 - Paper 1

Worked Solution & Example Answer:Kim is building a path around a garden at the back of a house, as shown - HSC - SSCE Mathematics Standard - Question 26 - 2023 - Paper 1

Find the area of the path.

Calculate how many 15 kg bags of cement Kim needs to buy.

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