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Question 1182521: A taxi firm charges a fixed cost of $10 together with a variable cost of $3 per mile.
(a) Work out the average cost per mile for a journey of 4 miles.
(b) Work out the minimum distance travelled if the average cost per mile is to be less than $3.25.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! total cost = 10 + 3m
m is the number of miles.
average cost per mile is equal to total cost / number of miles.
when you travel 4 miles, the total cost becomes 10 + 3 * 4 = 22.
the average cost per mile becomes equal to 22 / 4 = 5.5
when the average cost per mile is 3.25, then you get:
3.25 = total cost / number of miles.
since total cost = 10 + 3m, you get:
3.25 = (10 + 3m) / m.
multiply both sides of this eqaution by m to get:
3.25 * m = 10 + 3m
subtract 3m from both sides of the equation to get:
.25 * m = 10
divide both sides of the equation by .25 to get:
m = 10 / .25 = 40
the average cost per mile should be 3.25 when you have traveled 40 miles.
to confirm:
c = 10 + 3 * 40 becomes c = 10 + 120 which becomes c = 130.
that's your total cost.
average cost per mile becomes 130 / 40 = 3.25
the solution is confirmed to be good.
the average cost per mile will be 3.25 when you have traveled 40 miles.
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