A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

Discussion in 'Calculator Requests' started by math_celebrity, Oct 23, 2021.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?

    Declare variables:
    • Let a be the number of adult's tickets
    • Let c be the number of children's tickets
    Cost = Price * Quantity

    We're given two equations:
    1. a + c = 20
    2. 15a + 10c = 225
    Rearrange equation (1) in terms of a:
    1. a = 20 - c
    2. 15a + 10c = 225
    Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
    15(20 - c) + 10c = 225

    Solve for c in the equation 15(20 - c) + 10c = 225

    We first need to simplify the expression removing parentheses
    Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
    15 * 20 = (15 * 20) = 300
    15 * -c = (15 * -1)c = -15c
    Our Total expanded term is 300-15c

    Our updated term to work with is 300 - 15c + 10c = 225

    We first need to simplify the expression removing parentheses
    Our updated term to work with is 300 - 15c + 10c = 225

    Step 1: Group the c terms on the left hand side:
    (-15 + 10)c = -5c

    Step 2: Form modified equation
    -5c + 300 = + 225

    Step 3: Group constants:
    We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
    -5c + 300 - 300 = 225 - 300

    Step 4: Cancel 300 on the left side:
    -5c = -75

    Step 5: Divide each side of the equation by -5
    -5c/-5 = -75/-5
    c = 15

    Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
    a = 20 - 15
    a = 5
     

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