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

c stands for childs ticket
a stands for adults ticket

2c + 3a = 118
2a - 1/2c = 20 (multiply by -2 to get rid of fraction)
-4a + c = - 40
c = 4a - 40 ...now substitute 4a - 40 in for c in the first equation...

2c + 3a = 118
2(4a - 40) + 3a = 118
8a - 80 + 3a = 118
11a = 118 + 80
11a = 198
a = 18

now substitute 18 in for a in the second equation..
2c + 3a = 118
2c + 3(18) = 118
2c + 54 = 118
2c = 118 - 54
2c = 64
c = 32

answer : a (adults) = 18, c (children) = 32