508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $

Discussion in 'Calculator Requests' started by math_celebrity, Oct 14, 2020.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there?

    Assumptions:
    • Let the number of adults be a
    • Let the number of kids be k
    Given with assumptions:
    1. a + k = 508
    2. 2a + 1.25k = 885.50 (since cost = price * quantity)
    Rearrange equation (1) by subtracting c from each side to isolate a:
    1. a = 508 - k
    2. 2a + 1.25k = 885.50
    Substitute equation (1) into equation (2):
    2(508 - k) + 1.25k = 885.50

    Multiply through:
    1016 - 2k + 1.25k = 885.50
    1016 - 0.75k = 885.50

    To solve for k, we type this equation into our search engine and we get:
    k = 174

    Now, to solve for a, we substitute k = 174 into equation 1 above:
    a = 508 - 174
    a = 334
     

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