Casey is selling adult tickets and student tickets for the school play. The adult tickets cost $6.00 and the student tickets cos
t $4.00. Casey sells 120 tickets and makes $560.00. Which system of equations could be used to find the cost of each ticket?
1 answer:
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<h2><u>Answers:</u></h2>
These problems can be solved by the Thales’s Theorem, which states:
<em>Two triangles are similar when they have equal angles and proportional sides </em>
In addition, i<u>f two triangles are similar, their angles are similar as well</u>. This means that the relation between two sides of the big triangle is equal to the relation between two sides of the small triangle, as follows:
Knowing this, lets’s begin with the answers:
1. For this first problem, see the <u>first figure attached</u>. There are shown the two triangles, and we are told both are similar, this means (according the prior explanation above) that we can use the Thale’s Theorem to find .
Therefore, we can establish a relation between two sides of the big triangle which is equal to the relation between two sides of the small triangle; in this case let’s use and
for the first triangle and
and
for the second:
Now we find :
Finally, the value of is 12 units.
2. For this problem, see <u>the second figure attached</u>. In order to find the values of the segments BE and EC, we will use two sides of each triangle (ABE and DCE) according to the Thale’s Theorem:
<u>For the segment BE:</u>
Simplifying:
>>>>>This is the length of the segment BE
<u>For the segment EC:</u>
Simplifying:
>>>>>This is the length of the segment EC
3. For this problem, see the <u>third figure attached:</u>
Solving for :
Finally:
>>>>>This is the height of the smaller sail
4. For this problem, see the <u>fourth figure attached.</u>
Solving for :
>>>>>This is the height from the floor to the son's hand