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Question 1184509: The fee for hiring a guide to explore a cave is 700 pesos.A guide can only take care of a maximum of 3 persons,and additional guide can be hired as needed. Represent the cost of hiring guides as a function of the number of tuorists ho wish to explore the cave and plot its graph
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52898)   (Show Source):
You can put this solution on YOUR website! .
Everything is MORE than obvious.
Divide all existing tourists in groups by 3.
If all the groups are full, let n be the number of all such groups.
If the last group is not full, let the number of all groups, including one incomplete group, be n.
Then the fee is the product of 700 pesos by the number of groups, or 700*n.
Answered, solved and carefully/thoroughly explained.
If you think that it is not obvious, be the first to throw a stone at me . . .
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! Let x be the number of tourists in the trip. Then ⌈x/3⌉ gives the number of groups consisting of at most 3 tourists.
Note that the last group may not even consist of 3 tourists, but is considered a group nonetheless, since a guide
will be assigned to it and still be paid the 700 pesos. For example, if there are 511 tourists then there are ⌈511/3⌉ = ⌈170.333...⌉ = 171 groups,
although the last group has only 1 member tourist.
In other words, the cost of hiring guides as a function of the number of tourists x is given by C(x) = 700⌈x/3⌉.
*** ⌈x⌉ is called the least integer function, or ceiling function for x. Its graph is a 'step' function.
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