Question

select the correct answer.
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?
a. ( 22x + 14y geq 172 )
( x + y < 10 )
b. ( 22x + 14y > 172 )
( x + y leq 10 )
c. ( 14x + 22y geq 172 )
( x + y < 10 )
d. ( 14x + 22y > 172 )
( x + y leq 10 )

Explanation:

Step1: Analyze cost inequality

Let \( x \) be glass vases (\$22 each) and LXI1 be ceramic vases (\$14 each). Total cost is more than \$172, so \( 22x + 14y > 172 \).

Step2: Analyze total vases inequality

Total vases (glass + ceramic) are no more than 10, so \( x + y \leq 10 \).

Step3: Match with options

Check options: Option B has \( 22x + 14y > 172 \) (cost) and \( x + y \leq 10 \) (total vases), which matches.

Answer:

B. \( 22x + 14y > 172 \), \( x + y \leq 10 \)