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 Math Central Quandaries & Queries
 Question from Michelle, a student: I do not know what equation(s) should be used in order to obtain the answer(s) to this word problem. A bus was rented for a trip, the cost was dived equally amongst the passengers. During the trip, someone mentioned that if there were 9 more passengers, they would have paid each $5\$$less. Another mentioned that if there were 6 less passengers, they would have each paid 5\$$ more. What is the cost of renting the bus and how much must each passenger pay. Hi Michelle, You don't know the number of passengers, how much each paid or the cost of renting the bus. If you knew two of these then you could calculate the third. Thus for example if the number of passengers is$N$and each paid$C\$$then the cost of renting the bus would be N \times C\. Now look at the first passenger's comment "if there were 9 more passengers, they would have paid each 5\$$ less." That is if the number of passengers were $N+9$ then each would have to pay $(C-5)\$$to cover the cost of the bus so$(N+9) \times (C-5)\$= N \times C\$.$Expand and simplify this equation. What equation do you get from the second passenger's comment? Solve these equations for$N$and$C.\$