Two cooks purchased plates and cups at the same store. the first cook bought 4 plates and 5 cups for a total of $25.25. the second cook bought 7 plates and 3 cups for a total of $25.50. what is the price of a plate?

Let p represent the quantity of plates
Let c represent the quantity of cups

Cook 1: 4p + 5c = 25.25
Cook 2: 7p + 3c = 25.50

Use elimination method to solve:
-3(4p + 5c = 25.25) → -12p -15c = -75.75
 5(7p + 3c = 25.50) → 35p +15c = 127.50

Add the equations:     23p + 0c  = 51.75
Divide by 23 to solve for p:     p  = 2.25

the cost of plate is $2.25