At the homecoming football game, the Senior Class office sold slices of pizza for $0.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.50. How many slices did they sell?

1 Answer
EZ as pi
Aug 15, 2016

#165# pizza slices.

Explanation:

We do not know how many of each were sold, but we can use a variable to define the numbers.
(Use the smaller number as the variable because it is usually easier to multiply and add than divide or subtract.)

Let the number of hamburgers be #color(blue)x#.
Therefore the number of pizza slices is #color(red)(x+40)#

We are given the price of each item.

Value of all the#color(blue)(" hamburgers")# = #$1.35 xx x =color(blue)(1.35x)#
Value of all the #color(red)("pizza slices")# = #0.75 xx (x+40) = color(red)(0.75(x+40))#

The total of all the sales of hamburgers and pizza slices is given, so we can write an equation.
#"Money from " color(blue)("hamburgers") + "money from "color(red)("pizza slices") = color(green)(292.50.)#

#color(blue)(1.35x)+color(red)(0.75(x+40)) = color(green)(292.50)#

#1.35x+0.75x+30 = 292.50#

#2.1x = 292.5-30#

#2.1x=262.5#

#x = 125#

The number of hamburgers is 125, so 165 pizza slices were sold.

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