Question:
Tony buys 12 apples and 7 pears for £10.90. An apple costs 20p less than a pear. What would be the cost of 4 apple and 9 pears?
Methods:
Let’s call an apple ‘a’, and a pear ‘p’. If Tony bought 12 apples and 7 pears for £10.90, then we can write the following equation:12a + 7p = 10.9
If an apple costs 20p less than a pear, we can say: a = p – 0.2
Treating these as simultaneous equations, we can use the second equation to replace ‘a’ in the first equation with ‘p – 0.2’:
12(p – 0.2) + 7p = 10.9
This can be simplified:
12p – 2.4 + 7p = 10.9
19p = 13.3p = 0.7
Putting this value back into the second equation, we get: a = 0.7 – 0.2 which simplifies to: a = 0.5
So, an apple costs 50p and a pear costs 70p. Now, to find the cost of 4 apples and 9 pears:4 x 0.5 + 9 x 0.7 = 8.3
Answer:
£8.30
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