<h3>Answer: 8 people</h3>
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Work Shown:
x = number of people
y = cost per person
The cost per person varies inversely with the number of people, so y = k/x for some fixed number k.
"It costs $90 each for five people", meaning that x = 5 and y = 90 pair up. Plug these values in and solve for k.
y = k/x
90 = k/5
90*5 = k
450 = k
k = 450
Therefore the equation updates to y = 450/x
Now we want to know how many passengers there are (x) when the cost per person is y = 56.25
Let's find out:
y = 450/x
56.25 = 450/x ... replace y with 56.25
56.25x = 450
x = 450/56.25
x = 8
If you have 8 people, then it costs $56.25 per person.
side note: the total cost is $450 which is the value of k we found earlier. Divide 450 over 8 and you should get 56.25 exactly. Optionally you can turn y = k/x into x*y = k form. So the equation y = 450/x is the same as x*y = 450.
