SOLUTION: A group of 30 tourists paid a total of $686 in bus fares. If the adult fare was $28 and children paid half fare, how many adults were in the group?

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Question 772675: A group of 30 tourists paid a total of $686 in bus fares. If the adult fare was $28 and children paid half fare, how many adults were in the group?
Answer by pakhi(24) About Me  (Show Source):
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Let the number of adults in the group be A.
Let the number of children in the group be C.
Therefore according to the problem
Condition 1 A child's fare was half of that of an adult's fare i.e. 28/2= $14.

Condition 2 Total number of tourists were equal to 30
A + C = 30 or C = 30 - A ------------------(1)
Condition 3 Total bus fare was $686 which was equal to the bus fares of A adults @ $28 each plus the fares of C children @ $14 each
28A + 14C = 686
Putting the value of C from equation 1 we get
28A + 14(30 - A) = 686
or 28A + 420 - 14A = 686
or 14A = 686 - 420 = 266
or A = 266/14 = 19
Also C= 30 - A = 30 - 19 - 11
So the number of adults in the bus was 19 and the number of children was 11.