Triangle ABC has vertices A(1,4), B(-1,5), and C(1,-4). Triangle ABC is dilated and
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Answer:
Children: $13
Adults: $18
Step-by-step explanation:
Well for both sets we can set up the following system of equations,
So first we need to solve for a in the first equation.
3a + 4c = 106
-4c to both sides
3a = -4c + 106
Divide 3 by both sides
<u>a = -4/3c + 35 1/3</u>
Now we plug in that a for a in 2a + 3c = 75.
2(-4/3c + 35 1/3) + 3c = 75
-8/3c + 70 2/3 + 3c = 75
Combine like terms
1/3c + 70 2/3 = 75
-70 2/3 to both sides
1/3c = 4 1/3
Divide 1/3 to both sides
c = 13
Now we can plug in 13 for c in 3a + 4c = 106,
3a + 4(13) = 106
3a + 52 = 106
-52 to both sides
3a = 54
Divide 3 by both sides.
a = 18
<em>Thus,</em>
<em>an adult ticket is $18 and a children's ticket is $13.</em>
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<em>Hope this helps :)</em>