Question 1177790
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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....<br>
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.<br>
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.<br>
ANSWER: 5 first class and 2 coach<br>
CHECK: 5(970)+2(150) = 4850+300=5150<br>