Two fans went to the concession stand at halftime of game four. Fan D bought five hot dogs and four drinks for a total of 32$. Fan E bought three hot dogs and two drinks for a total of 18$. What is the price of a hot dog? What is the price of a drink?

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Answer 1 · 2016-09-05T23:52:30

The drink costs #$3#.

Let #x# be the cost of a hot dog, and #y# be the cost of a drink.

#5x + 4y = 32#
#3x + 2y = 18#

Solve by elimination:

#5x + 4y = 32#
#+ -2(3x + 2y) = -2(18)#

#5x + 4y = 32#
#-6x - 4y = -36#
#--------------------#
#-x = -4#

#x = 4#

#:.#A hotdog costs #$4#.

Substitute to solve for #y#.

#5x + 4y = 32#

#5(4) + 4y = 32#

#4y = 12#

#y = 3#

Hence, a drink costs #$3#.

Hopefully this helps!