Question

A flight company has a total luggage weight limit per passenger of 50 kg. Carol packed a suitcase weighing 20 kg, and she packed 3 rucksacks each weighing n kg. The combined weight of Carol's luggage was over the total weight limit. Without 1 of the rucksacks, the combined weight of Carol's luggage was at least 4 kg below the total weight limit. Write a double inequality to represent the possible values that n could take.

Answer 1

To represent the possible values of n, we set up the inequalities: 20 + 3n > 50 and 20 + 2n <= 50. Simplifying the second inequality gives 2n <= 30, and by dividing both sides by 2, we find that n <= 15.

Step-by-step explanation:

To represent the possible values of n, we need to consider the combined weight of Carol's luggage with and without one of the rucksacks. Let's set up the inequalities:

Combined weight with all rucksacks: 20 + 3n > 50

Combined weight without one rucksack: 20 + 2n <= 50

We can simplify the second inequality by subtracting 20 from both sides: 2n <= 30

Now, let's solve for n by dividing both sides by 2: n <= 15

So, the possible values for n are any number less than or equal to 15.