SOLUTION: Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 7 people took the trip. She was able to purchase
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Question 1177790: Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 7 people took the trip. She was able to purchase coach tickets for $150 and first class tickets for $970. She used her total budget for airfare for the trip, which was $5150. How many first class tickets did she buy? How many coach tickets did she buy? Found 2 solutions by mananth, greenestamps:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Sarah a total of 7 people took the trip.
let number of coach class tickets be x
first class tickets be y
x+y=7
She was able to purchase coach tickets for $150 and first class tickets for $970.
total budget $5150.
150x +970y = 5150
x + y = 7.00
150.00 x + 970.00 y = 5150.00 .............2
Eliminate y
multiply (1)by -970.00
Multiply (2) by 1.00
-970.00 x -970.00 y = -6790.00
150.00 x 970.00 y = 5150.00
Add the two equations
-820.00 x = -1640.00
/ -820.00
x = 2.00
plug value of x in (1)
x + y = 7.00
2.00 + y = 7.00
1.00 y = 5.00
y = 5.00
Ans x = 2.00
y = 5.00
2.00 coach class tickets
5.00 First class tickets
The response from the other tutor shows a formal algebraic solution -- although it is a mystery why she represented the numbers of coach tickets and first class tickets as numbers with two decimal places....
If a formal algebraic solution is not required and the speed of obtaining a solution is important, as in a timed math competition, there is a VERY quick and easy way to solve the problem using logical reasoning and a couple of easy mental math calculations.
The total cost of the tickets is a multiple of $50, and the cost of each coach ticket is a multiple of $50, so the total cost of the coach tickets is a multiple of $50. That means the total cost of the first class tickets, at $970 each, has to be a multiple of $50. With only 7 people on the trip, that means the number of first class tickets HAS TO be 5.
