Question

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?

Answer 1

X=number of plates
y=number of cups

4x+5y=25.25

7x+3y=25.50

Add the two equations together:

11x+8y=50.75
11x=50.75-8y

x=$\frac{50.75-8y}{11}$

Plug x into the first equation:
4x+5y=25.25

4( $\frac{50.75-8y}{11}$ ) = 25.25 

$\frac{4(50.75-8y)}{11}$ = 25.25

$\frac{203-32y}{11}$ = 25.25

203-32y = 277.75

-32y=74.75
32y=-74.45
y=2.34 (rounded to nearest hundredth)

The price of a plate is $2.34