Christmas sale
| Concepts | Algebraic fractions, forming equations, money, quadratic equations |
|---|---|
| KS3 curriculum | 3.1f |
| KS4 curriculum | 3.1e |
Resources
Christmas sale (worksheet)
Christmas sale (PowerPoint)Teaching notes
Ask questions to guide students towards the solution given below. Asking students to represent the information given in the question algebraically will help them to practise forming equations and expressions.
Solution
Let x be the original cost in pounds of 12 apples and n be the original number of apples per pound.
| Before discount: | 12/x = n |
| After discount: | 12/(x - 1) = n + 1 |
| Substitute for n: | 12/(x - 1) = 12/x + 1 |
| Multiply by x: | 12x/(x - 1) = 12 + x |
| Multiply by x - 1: | 12x = 12(x - 1) + x(x - 1) |
| Multiply out brackets: | 12x = 12x - 12 + x2 - x |
| Collect like terms: | 0 = x2 - x - 12 |
| Factorise: | 0 = (x - 4)(x + 3) |
Therefore the positive root is x = 4. The original price of the apples was £4 per dozen; the new price is £3 per dozen.
Extension
Discuss why the negative root (x = -3) is not applicable.
