Question

A) Three rucksacks have a combined weight of 57kg. Rucksack C is

2kg heavier than rucksack A, which is 1kg lighter than rucksack B.
What are the weights of each rucksack?



(b) Each person wants to carry the same weight of rucksack, but maintain 57kg across the three of them. What should happen to make the ratio of their rucksacks 1: 1: 1?

Answer 1

We can start by using the information given to set up a system of equations:

Let A, B, C be the weight of rucksacks A, B and C respectively

We know that:

C = A + 2 (C is 2kg heavier than A)

B = A + 1 (A is 1kg lighter than B)

A + B + C = 57 (Combined weight of all three rucksacks is 57kg)

We can substitute the second and third equations into the first one to get:

C = A + 2

B = A + 1

A + (A + 1) + (A + 2) = 57

3A + 3 = 57

3A = 54

A = 18

We can substitute this value of A back into the second and third equations:

B = 18 + 1 = 19

C = 18 + 2 = 20

So rucksack A weighs 18kg, rucksack B weighs 19kg and rucksack C weighs 20kg

(b) To make the ratio of the rucksacks 1:1:1, the weight of each rucksack should be 19kg. To achieve this, rucksack A should lose 1kg, rucksack B should gain 1kg and rucksack C should lose 2kg.

Explanation: