Respuesta :
Answer: the cost of one plate is $4.5
The cost of one cup is $2.1
Step-by-step explanation:
Let x represent the cost of 1 plate.
Let y represent the cost of 1 cup.
5 plates and 4 cups cost 30.90 dollars. It means that
5x + 4y = 30.9- - - - - - - -1
6 plates and 5 cups cost 37.50 dollars. It means that
6x + 5y = 37.5- - - - - - - -2
Multiplying equation 1 by 6 and equation 2 by 5, it becomes
30x + 24y = 185.4
30x + 25y = 187.5
Subtracting, it becomes
- y = - 2.1
y = 2.1
Substituting y = 2.1 into equation 1, it becomes
5x + 4 × 2.1 = 30.9
5x + 8.4 = 30.9
5x = 30.9 - 8.4
5x = 22.5
x = 22.5/5
x = 4.5
