Question

question 5 of 5
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. \\(\

$$\begin{cases} 22x + 14y \\geq 172 \\\\ x + y < 10 \\end{cases}$$

\\)
b. \\(\

$$\begin{cases} 14x + 22y > 172 \\\\ x + y \\leq 10 \\end{cases}$$

\\)
c. \\(\

$$\begin{cases} 22x + 14y > 172 \\\\ x + y \\leq 10 \\end{cases}$$

\\)
d. \\(\

$$\begin{cases} 14x + 22y \\geq 172 \\\\ x + y < 10 \\end{cases}$$

\\)

Explanation:

Step1: Analyze cost inequality

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

Step2: Analyze total vases inequality

Total vases ≤ 10, so \( x + y \leq 10 \).

Step3: Match with options

Option C has \( 22x + 14y > 172 \) and \( x + y \leq 10 \), which matches the inequalities.

Answer:

C. \(

$$\begin{cases} 22x + 14y > 172 \\ x + y \leq 10 \end{cases}$$

\)