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A group of k people rented a bus for an excursion. The bus company charged a fixed amount of $80 and an additional $6 for each person.(a) Find the cost of renting the bus in terms of k.Ans: (a) $k + $(b) The bus company charged the group of people $284 for the rental of a bus.Find the value of k.Ans: (b)

Question

A group of k people rented a bus for an excursion. The bus company charged a fixed amount of 80andanadditional80 and an additional 6 for each person.(a) Find the cost of renting the bus in terms of k.Ans: (a) k+k + (b) The bus company charged the group of people $284 for the rental of a bus.Find the value of k.Ans: (b)

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Solution

(a) The cost of renting the bus in terms of k can be found by adding the fixed cost to the variable cost per person. The fixed cost is 80andthevariablecostis80 and the variable cost is 6 per person. Therefore, the cost in terms of k is 80+80 + 6k.

(b) To find the value of k, we need to set up an equation using the total cost of the bus rental. We know that the total cost was 284andthatthecostintermsofkis284 and that the cost in terms of k is 80 + 6k.Therefore,wecansetuptheequation6k. Therefore, we can set up the equation 80 + 6k=6k = 284. Solving for k, we subtract 80frombothsidestoget80 from both sides to get 6k = 204.Then,wedividebothsidesby204. Then, we divide both sides by 6 to get k = 34. Therefore, the value of k is 34.

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