Edexcel GCSE Maths: Ratio and Proportion Worked Solutions

Question

7 kg of carrots and 5 kg of tomatoes cost a total of 480p. Cost of 1 kg of carrots : cost of 1 kg of tomatoes = 5 : 9. Work out the cost of 1 kg of carrots and the cost of 1 kg of tomatoes.

Worked Solution

1. 1

   Since the cost ratio is 5 : 9, let the cost per kg of carrots = 5k pence and per kg of tomatoes = 9k pence.

2. 2

   The total cost is 7 × 5k + 5 × 9k = 35k + 45k = 80k pence.

3. 3

   Set 80k = 480, so k = 6.

4. 4

   Cost of 1 kg carrots = 5 × 6 = 30p. Cost of 1 kg tomatoes = 9 × 6 = 54p.

Question

There are 48 counters in a bag. There are only red counters and blue counters in the bag. number of red counters : number of blue counters = 1 : 2 Helen has to work out how many red counters are in the bag. She says, "There are 24 red counters in the bag because 1 is half of 2 and 24 is half of 48" Is Helen correct? You must give a reason for your answer.

Worked Solution

1. 1

   Helen is not correct. A ratio of 1 : 2 means 1 part red and 2 parts blue — 3 parts in total.

2. 2

   Each part = 48 ÷ 3 = 16 counters.

3. 3

   Number of red counters = 1 × 16 = 16 (not 24). Helen incorrectly treated the ratio as if it were 1 : 1.