Word problem. Solve for two variables.

Question

A store sold plastic cups for $3.50 each and glass cups for $4 each. If 400 cups were sold for a total of $1456, how many cups of each type were sold. What was the dollar value of each type of cup sold? Thank you! 

Answer 1

p - plastic cups

g - glass cups

 

Total number of cups equation

p + g = 400

 

Total cost equation

3.5p +4g =1456

 

We solve the system and find

p =288

g =112.

 

The store sold 288 plastic cups and 112 glass cups.

 

Answer 2

Let x = # of plastic cups

400 - x = # of glass cups

 

3.50x + 4(400 - x) =1456

3.50x + 1600 - 4x = 1456

-0.5x= -144

x = 288

 

288 plastics cups were sold for a total of $1,008 and 112 glass cups were sold for a total of $448