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Math Help - Problem Solving: Using Systems

  1. #1
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    Post Problem Solving: Using Systems

    1. Kerry asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?

    2. Tickets for the homecoming dance cost $20 for a single ticket or $35 for a couple. Ticket sales totaled $2280, and 128 people attended. How many tickets of each type were sold?

    3. Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles.
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  2. #2
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    Quote Originally Posted by mjp1991 View Post
    1. Kerry asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?

    Total bills: T+F=15

    Total amount: 20T+50F=390

    Quote Originally Posted by mjp1991 View Post

    2. Tickets for the homecoming dance cost $20 for a single ticket or $35 for a couple. Ticket sales totaled $2280, and 128 people attended. How many tickets of each type were sold?

    Total tickets sold: S + C = 128

    Total amount collected: 20S+35C=2280

    Quote Originally Posted by mjp1991 View Post

    3. Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles.

    Sum of the angles: B+B+V=180

    If vertex angle is 40 degrees less than the sum of the measures of the base angles:

    V=B+B-40
    Now, how good are you at solving systems of linear equations?
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    i cant figure out the 3rd problem ):
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    #3

    B+B+V=180 (Sum of two base angles and vertex angle=180)

    (1) 2B+V=180

    ----------------------------------

    V=B+B-40 (Vertex angle = 40 less than sum of base angles)

    (2) V=2B-40

    Substitute this value for V into 2B+V=180 to get this:

    2B+(2B-40)=180

    4B=220

    \boxed{B=55}

    Substituting this answer into V=2B-40, we have V=2(55)-40 and \boxed{V=70}

    Each of the two base angles is 55^{\circ} and the vertex angle is 70^{\circ}
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