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13 July, 19:22

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 11 people took the trip. She was able to purchase coach tickets for $230 and first class tickets for $980. She used her total budget for airfare for the trip, which was $7780. How many first class tickets did she buy? How many coach tickets did she buy? number of first class tickets bought? number of coach tickets bought?

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  1. 13 July, 19:31
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    Sarah purchased 4 coach tickets and 7 First class tickets.

    Step-by-step explanation:

    Let the total number of coach tickets brought = x

    Let the total number of first class ticket purchased = y

    ⇒ x + y = 11

    Also, cost of 1 coach ticket = $230

    So, the cost of x coach tickets = x ($230) = 230 x

    And, cost of 1 first class ticket = $980

    So, the cost of y first class tickets = y ($980) = 980 y

    The total allowance for the trip is = $7780

    ⇒ 230 x + 980y = $7780

    Solving the given system of equation:

    x + y = 11

    230 x + 980 y = $7780

    Substitute the value y = 11 - x in the second equation.

    we get:

    230 x + 980 y = $7780 ⇒ 230 x + 980 (11 - x) = $7780

    or, 230 x + 10,780 - 980 x = 7780

    or, - 750 x = - 3000

    or, x = 3000/750 = 4

    or, x = 4

    ⇒ y = 11 - x = 11 - 4 = 7

    or, x = 4, y = 11 is the solution of the system.

    Hence, Sarah purchased 4 coach tickets and 7 First class tickets.
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