# Thread: Problem Solving: Using Systems

1. ## 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.

2. Originally Posted by mjp1991
1. Kerry asked a bank teller to cash a $390 check using$20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Total bills:$\displaystyle T+F=15$Total amount:$\displaystyle 20T+50F=390$Originally Posted by mjp1991 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: $\displaystyle S + C = 128$

Total amount collected: $\displaystyle 20S+35C=2280$

Originally Posted by mjp1991

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: $\displaystyle B+B+V=180$

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

$\displaystyle V=B+B-40$
Now, how good are you at solving systems of linear equations?

3. i cant figure out the 3rd problem ):

4. #3

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

(1) $\displaystyle 2B+V=180$

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

(2) $\displaystyle V=2B-40$

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

$\displaystyle 2B+(2B-40)=180$

$\displaystyle 4B=220$

$\displaystyle \boxed{B=55}$

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

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