Tim has \( \$ 20 \) to buy snacks for 12 people in an office. Each person will get one snack. Tim is buying bags of pretzels that cost \( \$ 1.50 \) per bag and bags of crackers that cost \( \$ 2.00 \) per bag. Part A Tim is buying \( x \) bags of pretzels and \( y \) bags of crackers. Which system of equations can be used to find the value of \( x \) and \( y \) ? (A) \( \left\{\begin{array}{r}x+y=20 \\ 1.5 x+2 y=12\end{array}\right. \) (B) \( \left\{\begin{array}{r}x+y=20 \\ 2 x+1.5 y=12\end{array}\right. \) (c) \( \left\{\begin{array}{r}x+y=12 \\ 1.5 x+2 y=20\end{array}\right. \) (D) \( \left\{\begin{aligned} x+y & =12 \\ 2 x+1.5 y & =20\end{aligned}\right. \)

To solve the problem, Tim needs a system of equations that reflects both the number of snacks he wants to buy (which is 12) and the total amount he can spend (which is $20). The correct option is: (D) \( \left\{\begin{aligned} x+y & =12 \\ 2 x+1.5 y & =20\end{aligned}\right. \) In this system, \( x \) represents the number of bags of pretzels, and \( y \) represents the number of bags of crackers. The first equation accounts for the total number of snacks (12), while the second equation represents Tim's budget ($20). Have you ever found yourself in a snack dilemma like Tim's? When planning for events, a good tip is to keep track of both quantity and budget. It can be useful to create a simple table listing snack types, how much each costs, and the total number of snacks needed. This way, you avoid overspending and ensure everyone's well-fed, all while keeping the snack game strong!