There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7in or 12in. The diameter of all 15 plates combined is 140in. Which system of equations can be used to find the number of 7in plates, x , and the number of 12in plates, y , that are in the cabinet?

Number of 7 inch plate = 8

Number of 12 inch plate = 7

Step-by-step explanation:

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7in or 12in. The diameter of all 15 plates combined is 140in. Which system of equations can be used to find the number of 7in plates, x , and the number of 12in plates, y , that are in the cabinet?

Given that :

Total Number of plates = 15

Diameter of each plate : 7 in or 12 in

Diameter of all 15 plates = 140 in

Let number of 7 in and 12 in diameter plates = x and y respectively ;

x + y = 15 - - (1)

7x + 12y = 140 - - - (2)

x = 15 - y

Substitute x = 15 - y in (2)

7(15 - y) + 12y = 140

105 - 7y + 12y = 140

105 + 5y = 140

5y = 140 - 105

5y = 35

y = 7

From x = 15 - y

x = 15 - 7

x = 8

Number of 7 inch plate = 8

Number of 12 inch plate = 7