Question

A magic show sold tickets for $2 for every child and $3 for every adult. The total sales were $118. The difference of two times the number of adults and half the children will total 20. Using the elimination method for the system of equations, what is the number of adults and children at the magic show?
A. adults = 5 children = 30
B. adults = 18 children = 32
C. adults = 16 children = 35
D. adults = 32 children = 18

Answer 1

@tester97

Answer 2

You could calculate which sets equal $118 by multiplying the number of adults by 3 added with the number of children times 2 and then add together, but there are probably more than one answer that supports that. The real different is your third sentences. The difference (meaning subtration) of two times the number of adults (2 x numofadults) and half the children (1/2 numofchildren) will total 20 (=20). Put it together and you have 2x-(1/2)y=20

Answer 3

Here is an easier way:
c stands for child and a stands for adult
3a + 2c = 118 --> (2) 3a + 2c = 118)
2a - 1/2c = 20 --> (-3)2a - 1/2c = 20
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6a + 4c = 236 (result of multiplying by 2)
-6a + 1.5c = - 60 (result of multiplying by -3)
-------------add
5.5c = 176
c = 32

now sub 32 in for c in either of the original equations..
3a + 2c = 118
3a + 2(32) = 118
3a + 64 = 118
3a = 118 - 64
3a = 54
a = 18

Answer 4

let's write the equations:

Let C be the number of children's tickets sold
Let A be the number of adult's tickets sold

2*C + 3*A = 118 - total sales, with children's tickets at $2 each and adults at $3 each

the difference of two times the number of adults and half the children = 20
2A - 1/2 C = 20

So you have a system of two equations:

3A + 2C = 118
2A - (1/2)C = 20

I would suggest multiplying the second equation by 4 and adding the two equations. This will give you an equation only in terms of A.