one shuttle service charges $10 for pickup and $0.10 per mile.the other shuttle service has no pick up fee but charges $0.35 per mile. find the number of miles for which the cost of the shuttle service is the same.
let m be the number of miles
.35m = 10 + .1m
.25m = 10
m = 10/.25 = 40 miles
Shrek's toenails
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Well, I have to say, these shuttle services sure know how to keep things interesting with their pricing! It's like a race to see who can confuse us more.
Alright, let's crunch the numbers and find out when the costs are the same. We'll call the number of miles "x".
For the first shuttle service, the cost is $10 for pickup plus $0.10 per mile. So the total cost would be 10 + 0.10x.
As for the second shuttle service, there's no pickup fee, which is a relief to our wallets. But they charge $0.35 per mile. So the total cost would just be 0.35x.
Now, if we want to find when the costs are the same, we can set up an equation:
10 + 0.10x = 0.35x
Okay, now let's subtract 0.10x from both sides to get rid of that sneaky variable hanging out with the 10:
10 = 0.25x
And now, let's divide both sides by 0.25 to solve for x:
x = 40
So, after all that mathematical madness, it turns out that the two shuttle services would cost the same for a 40-mile trip. Can you believe it? 40 miles! They really don't make this easy for us, do they?
To find the number of miles for which the cost of the shuttle service is the same, we need to set up an equation and solve for the variable representing the number of miles.
Let's assume the number of miles is represented by 'x'.
For the first shuttle service, the cost is composed of a pickup fee of $10 and $0.10 per mile. Therefore, the cost of the first shuttle service can be represented as:
Cost of first service = $10 + ($0.10 * x)
For the second shuttle service, there is no pickup fee, but the cost is $0.35 per mile. Therefore, the cost of the second shuttle service can be represented as:
Cost of second service = $0.35 * x
To find the value of 'x' for which the costs are the same, we can set up the equation:
$10 + ($0.10 * x) = $0.35 * x
Now, let's solve the equation to find the value of 'x'.
Subtract $0.10 * x from both sides of the equation to isolate the constants on one side:
$10 = $0.35 * x - $0.10 * x
Combine like terms:
$10 = $0.25 * x
Finally, divide both sides of the equation by $0.25 to solve for 'x':
$10 / $0.25 = x
x = 40
Therefore, the cost of both shuttle services will be the same for a distance of 40 miles.