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

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, right?  Which answer solves this equation?