One hiking club charges $20 to become a member and $5 to participate on each hike. Anotherclub charges no membership fee, but charges $7 to participate on each hike. How many hikes must you go on to make the first club more economical ?(:
Just make up a table of cost vs number of hikes for each club
#Hikes #1 Cost #2 Cost
0 20 0
2 30 14
4 40 28
6 50 42
8 60 56
10 70 70
The club with the membership fee is more economical if you take more than 10 hikes.
11. It is $20 to start, every hike, you are charged $2 more from the second company. If you divide 20 by 2, 10 will be even and at 11 it will be 2 $ more.
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.
To determine how many hikes you must go on to make the first club more economical, we can compare the costs of both clubs based on the number of hikes.
Let's assume the number of hikes you plan to go on is represented by 'x'.
For the first club (with a $20 membership fee and $5 per hike):
The cost of becoming a member: $20
The cost per hike: $5
Therefore, the total cost for the first club after x hikes would be:
Total cost = Membership fee + (Number of hikes × Cost per hike)
Total cost = $20 + (x × $5)
Total cost = $20 + 5x
For the second club (with no membership fee, but $7 per hike):
The cost per hike: $7
Therefore, the total cost for the second club after x hikes would be:
Total cost = Number of hikes × Cost per hike
Total cost = x × $7
Total cost = 7x
To find out when the cost of the first club becomes more economical, we need to set up an equation and solve for x:
20 + 5x < 7x
Subtract 5x from both sides:
20 < 2x
Divide both sides by 2:
10 < x
Therefore, you would need to go on at least 11 hikes for the first club to become more economical than the second club.