At a movie theatre, tickets for two adults, two seniors, and two children cost $46. Tickets for one senior and two children cost $19.50. Tickets for one adult, one senior, and three children cost $36.00. What is the cost of each ticket? I think know the cost from guess and check, but I need an equation. I have over 10 pages worth of nothing. Please help!!
I'm in a graduate math course and having troubles. I'm a reading teacher working on my math endorsement.headache
Simultaneous equations.
Let a = adult price, c=child price, s= senior price,
(eqn1) 2a + 2c + 2s = $46
(eqn2) s + 2c = $19.50
(eqn3) a + s + 3c = $36 =%26gt; 2a + 2s +6c = $72 (multiply both sides by 2)
So: 2x(eqn3) - (eqn1)
=%26gt; 2a + 2s +6c 鈥?2a - 2c - 2s = $72 - $46
=%26gt; 4c = 26 =%26gt; c = $26/4= $6.50
By (eqn2)
s = $19.50 鈥?2c = $19.50 鈥?2 x $6.50= $19.50 - $13.00 = $6.50
(eqn1) 鈥?(eqn2)
=%26gt; 2a + 2c + 2s 鈥?s 鈥?2c = $46 - $19.50
=%26gt; 2a +s = $26.50
=%26gt; 2a = $26.50 鈥?s = $26.50 - $6.50 = $20
=%26gt; a = $20 / 2 = $10
So Adults $10, Children $6.50 and Seniors $6.50
Check
(eqn1) 2 x $10 + 2 x $6.50 + 2 x $6.50 = $20 + $13 + $13 = $46
(eqn2) s + 2c = $6.50 + 2 x $$6.50 = $6.50 + $13.50 = $19.50
(eqn3) a + s + 3c = $10 + $6.50 + 3 x $6.50 = $10 + $6.50 + $19.50 = $36
I'm in a graduate math course and having troubles. I'm a reading teacher working on my math endorsement.paramount theater opera theater
Let adults = a, seniors = s, children = c.
From what the problem gives:
2a + 2s + 2c = 46
s + 2c = 19.5
a + s + 3c = 36
So now we have 3 variables and 3 equations (recall systems of equations with 3 variables). There's several ways to go about solving them, the easiest probably being matrices (if you have a calculator) or by solving for each variable and substituting.
s=senior; c=children; a=adults
2s+2a+2c=46
2s+ 2(36-s-3c)+2c=46
2s+72-2s-6c+2c=46
72-4c=46
-4c=-26
c=6.5
s+2c=19.50
s+2(6.5)=19.5
s+13=19.5
s=6.5
2(6.5)+2a+2(6.5)=46
13+2a+13=46
2a=20
a=10
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