To determine how many hikes you must go on to make the first club more economical, we need to set up an equation.
Let's assume you want to compare the total cost of participating in the first club with the total cost of participating in the second club.
For the first club, the total cost can be calculated as the sum of the membership fee ($20) and the cost per hike ($5) multiplied by the number of hikes.
First Club total cost = $20 + $5 × number of hikes
For the second club, the total cost can be calculated as the cost per hike ($7) multiplied by the number of hikes.
Second Club total cost = $7 × number of hikes
To find the number of hikes at which the first club becomes more economical, we need to set up an equation where the total cost of the first club is equal to or less than the total cost of the second club.
$20 + $5 × number of hikes ≤ $7 × number of hikes
Simplifying the equation:
$20 ≤ $7 × number of hikes - $5 × number of hikes
$20 ≤ $2 × number of hikes
Now, divide both sides of the equation by $2:
$10 ≤ number of hikes
Therefore, you must go on at least 10 hikes to make the first club more economical than the second club.