Question 441073: Hello, can someone please help me on this question.
A railway company charge passengers $75 each for a journey. All of the passengers except for 31 decide to pay an additional $15 each for an optional lunch. Altogether the company recieves $10,425 from the passengers. Suppose there are x passengers. Write down an equation and solve it to work out the number of passenger.
I have tried this problem and i came up with 121 passengers. i need an equation though and i would like to know if that is correct?
Thank-you for your help :)
Answer by Mlallory_Pl(3)   (Show Source):
You can put this solution on YOUR website! A bunch of people are going for a train ride. There are X people on the train, total. X people paid the $75 for the ride. X-31 people ALSO paid $15 for lunch. The railroad received $10,425. Right? Stop now and get your head around it or it will not help you. OK -- Let's solve this!
75x + 15(x-31) = 10425
75x + 15x - 465 = 10425 we multiplied the 15 by all that was inside the ( )
90x - 465 = 10425 we added the 75x and the 15x (like terms)
90x - 465 + 465 = 10425 + 465 when we put an = in an equation, it enables us to do anything we want to either side of the equation -- as long as we do the SAME THING to the other side of it. Here, we added 465 to both sides to get all the variables (90x) on one side and the constants (10425 + 465) on the other side. Now it becomes more simple!
90x = 10890
90x / 90 = 10890 / 90 we divide both sides by 90. we know what 90 x's are, we want to know what 1 x is.
x = 121. There were 121 people on the train. Let's check our answer just for fun.
121 X $75 = $9,075 121 - 31 paid $15 more. How many people was that? 90. 90 X $15 = $1350
$9,075 + $1,350 = $10,425!
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