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25 September, 02:10

2000 tickets were sold in an exhibition on Saturday. The cost of a ticket for an adult is $4 and for a child is $2. The total amount collected on Saturday was $6400. Find the number of adult tickets and child tickets sold on Saturday.

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  1. 25 September, 04:57
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    Let x = # of adult tickets sold (at $4.00 each)

    Let y = # of child tickets sold (at $2.00 each)

    We can take the above information, along with the 2000 tickets sold and the $6,400 collected, to get the following two math statements:

    x + y = 2000 (Total unknown number of $4.00 + total unknown number of $2.00 tickets, equals a total of 2,000 tickets sold

    4x + 2y = 6400 ($4.00 * unknown number of $4.00 tickets + $2.00 * unknown number of $2.00 tickets, equals the total of $6,400 collected in ticket sales

    So, write these as:

    x + y = 2000

    4x + 2y = 6400

    Take the first equation: Turn it into a y = statement, by subtracting 'x' from both sides, to get:

    y = 2000 - x

    Next, go to the 2nd equation. Where you see the 'y', substitute the y-value in its place: '2000 - x'

    This gives you:

    4x + 2 (2000 - x) = 6400

    This then gives us: 4x + 4000 - 2x = 6400

    Collect like terms to get:

    2x + 4000 = 6400

    Subtract 4000 from both sides to get:

    2x = 2400

    Next, divide both sides by 2, to get x = 1200

    We now know that there were 1,200 adult ($4.00) tickets sold; put this information back into the original equation:

    1200 + y = 2000

    Next, subtract 1200 from both sides, so that we can solve for y; which is:

    y = 800

    Next, check our work, by substituting back into the two original equations:

    1200 + 800 = 2000 [Check]

    4 * 1200 + 2 * 800 = 4800 + 1600 + 6400 [Check]

    So: 1,200 tickets sold at $4.00 each; and 800 tickets sold at $2.00 each, final and correct answer.
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