# Calculating Turf Costs

#### Charlie4254

##### New member
I've been sitting here for about an hour trying to work this out and I give up. Not sure if I'm being stupid or what but here it is.

So I need to come up with a formula that calculates the price of turf for someone's garden.

The customer will give us the length and width of their garden in meters.
Turf is sold in 1m x 0.6m rolls for £2.50 each
Must add 10% of the total number of rolls of turf to allow for wastage

#### Subhotosh Khan

##### Super Moderator
Staff member
I've been sitting here for about an hour trying to work this out and I give up. Not sure if I'm being stupid or what but here it is.

So I need to come up with a formula that calculates the price of turf for someone's garden.

The customer will give us the length and width of their garden in meters.
Turf is sold in 1m x 0.6m rolls for £2.50 each
Must add 10% of the total number of rolls of turf to allow for wastage
Is this a homework problem from school or work problem?

Give us a typical request from a customer - and we will build from there.

#### Romsek

##### Full Member
What I'd do, since this is real life. I'd round the specs up to the nearest meter by 3 meters.
5 rolls is 1m x 3m.
$$\displaystyle \text{Let the clients specs be \ell_{spec} \times w_{spec}}\\ L=3\left(\left \lfloor \dfrac{\ell}{3} \right\rfloor + 1\right)\\ W=\left \lfloor w\right\rfloor + 1\\ N_\ell = \left \lceil 5 \cdot \dfrac{L}{3} \cdot 1.1 \right \rceil\\ N_w = \lceil W \cdot 1.1 \rceil\\ \text{You would need to purchase N_\ell \times N_w rolls of sod}$$

Do you understand the symbols I used?

$$\displaystyle \lfloor x \rfloor = \text{the largest integer less than x}\\ \lceil x \rceil = \text{the least integer larger than x}\\ \text{for example, \lfloor 10.4 \rfloor = 10}\\ \text{\lceil 10.4 \rceil = 11}$$

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#### HallsofIvy

##### Elite Member
The area of the lawn is lw, "length times width", which the customer tells you. The area of each roll is (1)(0.6)= 0.6 square meters. The number of rolls needed is $$\displaystyle \frac{lw}{0.6}$$ and the cost of those rolls is £$$\displaystyle \frac{2.5lw}{0.6}$$. To add 10% for wastage multiply that by 1.1: £$$\displaystyle \frac{2.75lw}{0.6}$$. I would not round since you are adding "10% for wastage".