IMC 2015 Q18
18. The total weight of a box, 20 plates and 30 cups is 4.8 kg. The total weight of the box, 40 plates and 50 cups is 8.4 kg. What is the total weight of the box, 10 plates and 20 cups?
- A 3 kg
- B 3.2 kg
- C 3.6 kg
- D 4 kg
- E 4.2 kg
Intermediate Mathematical Challenge 2015, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 3 kg
Let the weights in kg of the box, 1 plate and 1 cup be \(b\), \(p\) and \(c\) respectively.
Then: \(b + 20p + 30c = 4.8\) (i); \(b + 40p + 50c = 8.4\) (ii).
Subtracting (i) from (ii): \(20p + 20c = 3.6\) (iii). So \(10p + 10c = 1.8\) (iv).
Subtracting (iv) from (i): \(b + 10p + 20c = 3\). So the required weight is 3 kg.
Solution © UK Mathematics Trust, from the IMC 2015 solutions. Longer versions with investigations: Solutions and investigations (PDF).