Ben is decorating his home with vases of flowers. He bought glass vases that cost $22 each and ceramic vases that cost $14 each. The total cost of the vases came to more than $172. Also, Ben bought no more than 10 vases in all. Which system of inequalities can be used to determine the number of glass vases, x, and the number of ceramic vases, y, that Ben could have bought?

Step-by-step explanation:

x + y = 10

22x + 14y = 172

-22x - 22y = -220

22x + 14y = 172

-8y = - 48

y = 6 ceramic vases

x + 6 = 10

x = 4 glass vases

Step-by-step explanation:

cost of glass vases x=22 $

cost of ceramic vases y=$14

22x+14y >172

or 11x+7y>86

x+y≤10

x   y          11x+7y

1   9            11+63=74

2  8            22+56=78

3  7            33+49=82

4   6           44+42=86

5   5          55+35=90

6   4          66+28=94

7   3          77+21=98

8  2          88+14=102

9  1          99+7=106

he can buy glass vases in the following combinations .

(x,y)→(5,5),(6,4),(7,3),(8,2),(9,1)

if x = 1, then the answer is 3.5