l = 2w - 4
Because we're solving for 2l + 2w, that can be simplified to
2(2w - 4) + 2w = 34
4w - 8 + 2w = 34
6w - 8 = 34
6w = 42
w = 7
Knowing this, we can input w:
2(7) + 2l = 34
14 + 2L = 34
2l = 20
l = 10
L = 10, W = 7, Option C
<u>Let's consider the facts at hand</u>:
- By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
- ∠BEC = ∠DFC
- Sides BE = DF
<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
<em>Definitions of Theorem I used:</em>
- <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
- <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>
<em />
With a 12% discount, 18.48 is the price per ticket (2.52 per ticket saved). In order to determine the amount of tickets, we divide the saved amount by the amount saved per ticket.
819/2.52 is 325.
There were 325 tickets purchsed.
2+3+4+5+y+7+8+9+10c11+12+13+14+15
