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

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

anonymous · Answer

The answer is B, because the difference of two times the number of adults (36) and half the children (16) = 36-16 = 20. Also they add up to $118.
Do you know how I got this, Brittany?

anonymous · Answer

Need anything else?

texaschic101 · Answer

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
-------------
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

Daniel_F is correct...the answer is B.

anonymous · Answer

@texaschic101 :)