"A gardener has been asked to lay a patio 3 metres longer than its width. Each slab is a square of side 0.5 metres and costs £4. The gardener has been asked to spend more than £220 but less than £448. Find the two possible amounts he could spend."
So I know that, for the patio, the length will be 3+w and the width will be w, i do not know where to go from there.
That's good, so far. Next, you need to determine an expression (using symbol w) that represents the total number of 0.5 meter by 0.5 meter slabs it will take to create an area equal to the area of the w+3 meter by 3 meter patio. That's a division problem.
For example, if I had an area of 300 square meters, and I wanted to cover it with 2 by 2 meter squares, I would divide the big area by the small area (300/4), to calculate a total of 75 squares needed.
What expression can you write, for the area of the patio?
What expression can you write, for the area of a single slab?
Divide the patio area by the slab area, and you will have an expression representing the number of slabs needed.
Multiply the number of slabs by 4, to get an expression for the total cost of those slabs. Once you have an expression for the total cost, write and solve two inequalities, using the lower (given) pound amount for one and the higher pound amount for the other).
Then think about the solutions for w. That is, consider these two possible widths of the patio, and remember that the slabs are 0.5 meter squares. You need to have a whole number of slabs along the patio's width (i.e., cutting slabs to fit is not allowed), and the total cost must be strictly
inbetween £220 and £448.
In order to accommodate all of the constraints, there are only two possibilities for the width of the patio. Substitute each of these values for w into the expression for total cost, evaluate, and you will have your answers.
If you need more help, please continue showing your work. If I wrote anything that you don't understand, let us know. :cool:
