Question

"There are 17 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 17 plates combined is 159 inches. How many 7-inch plates are in the cabinet?

a. 9
b. 7
c. None of these
d. 21

Answer 1

To solve this problem, we need to set up an equation using the total number of plates and the sum of their diameters as information. By solving this system of equations, we can determine the number of 7-inch plates in the cabinet.

Step-by-step explanation:

To solve this problem, we need to set up an equation. Let's assume there are x plates with a diameter of 7 inches and y plates with a diameter of 12 inches. We can set up the following two equations:

1. x + y = 17 (since there are a total of 17 plates)
2. 7x + 12y = 159 (since the sum of the diameters of all plates is 159 inches)

Next, we can solve these equations simultaneously. By multiplying the first equation by 7, we get:

7x + 7y = 119

Subtracting this equation from the second equation, we eliminate the variable x:

12y - 7y = 159 - 119

5y = 40

Dividing both sides of the equation by 5, we find:

y = 8

Finally, substituting this value back into the first equation:

x + 8 = 17

x = 9

Therefore, there are 9 7-inch plates in the cabinet. The correct answer is a. 9.