Unit 5 sec 1.2 finding and simplifying formulas

Unit 5 sec 1.2 finding and simplifying formulas

15 December 2015

23:40

Suppose that a baker makes a particular type of loaf. Each loaf cost 69p to make, and is sold for £1.24. The baker sells all the Loaves that he makes.

On a particular day, the baker makes 30 loaves. Let us calculate the profit that he makes from them. The total cost, in £, of making the loaves is

30 × 0.69 =20.70

the total of money, in £, paid for the loaves is

30 × 1.24 =37.20

so the profit in £ is given by

37.20 – 20.70 = 16.50

that is, the profit is £16.50.

  It will not be useful for him to have a formula to help him calculate the profit made from any number of loaves. To obtain the formula, we represent the number of loaves by a letter, say n, and worked through the same calculation as above, but using n in place of 30.

The total cost, in £, of making the loaves is

N ×0.69 =0.69n.

The total number of money, in £, paid for the loaves that customers is

N × 1.24 =1.24n.

So if we represent the profit by £p, then we have the formula

P = 1.24n -0.69n.

 The formula makes it easy to calculate the profit, because you do not need to think through the details of the calculation. You just substitute in the number and do the numerical calculation. This is the advantage of using a formula.

  In fact, the task of calculating the profit can be made even more straightforward. It is possible to find a simpler formula for p, by looking at the situation in a different way. The profit, in £, for each loaf of bread is

1.24 – 0.69 =0.55

so the profit, in £, for n loaves of bread is

n ×0.55 = 0.55n.

So we have the alternative formula

P = 0.55n.

The alternative formula of the profit is better because it is simpler and using it involves calculations.

   In this case, a simpler formula was found by thinking about the situation in a different way. However, it is often easier to find whatever formula you can, and then use algebra to turn it into a simpler form.

  Algebra can also help you to find formulas. The formula that the baker’s profit was obtained directly from the situation that it describes, but it is often easier to obtain formulas by using other formulas that you know already. Algebra is needed for this process and it is also needed to turn the new formula into a simpler form.