Question

Teddy's garden is in the shape of a rectangle with the dimensions 4.2 m and 1.8 m. Teddy's dad wants to cover the entire garden with turf to make a lawn. Each piece of turf measures 60 cm by 60 cm. They are available in three different pack sizes. Pack of 12: £85.20 Pack of 6: £44.40 Individual: £7.52 What is the cheapest way to cover the garden with turf? How much will it cost?​

Answer 1

Answer:

The cheapest way to cover the garden is with a 12-pack, a 6-pack, and 3 individual pieces of turf.

This will cost £152.16.

Step-by-step explanation:

We are given that the garden is in the shape of a rectangle with dimensions 4.2 m by 1.8 m. The entire garden is to be covered with turf, and each square piece of turf measures 60 cm × 60 cm. The turf is available in various packs with differing prices.

To determine the cheapest way to cover the garden with turf, we first need to calculate the number of pieces of turf required.

Start by dividing the width and length of the garden by the side length of each square piece of turf. Since the garden dimensions are given in metres and the turf dimensions are given in centimetres, convert the metres to centimetres by multiplying them by 100.

$\textsf{Number of pieces of turf along width}=\dfrac{1.8 \times 100}{60}=3$

$\textsf{Number of pieces of turf along length}=\dfrac{4.2 \times 100}{60}=7$

Therefore, we need exactly 3 pieces of turf along the width of the garden and 7 pieces of turf along its length. So, the total number of pieces of turf needed is:

$\textsf{Total pieces of turf}=3 \times 7=21$

Now, we need to determine the price per piece of individual turf for the multi-packs by dividing the price per pack by the number of pieces it contains:

$\textsf{Pack of 12: Price per piece}=\dfrac{\£85.20}{12}=\£7.10$

$\textsf{Pack of 6: Price per piece}=\dfrac{\£44.40}{6}=\£7.40$

Given that the price of an individual piece of turf is £7.52, we can see that the price per piece decreases as the pack size increases. Therefore, the cheapest way to cover the garden is by buying 21 pieces as a combination of a 12-pack, a 6-pack, and 3 individual pieces.

$\textsf{Total cost}=\textsf{12-pack}+\textsf{6-pack}+\textsf{3 individual pieces}\\\\\\\textsf{Total cost}=\£85.20+\£44.40+3 \times \£7.52\\\\\\\textsf{Total cost}=\£85.20+\£44.40+ \£22.56\\\\\\\textsf{Total cost}=\£152.16$

Therefore, it will cost £152.16 to cover the garden with turf in the cheapest way possible.