To determine the appropriate system of equations for the given problem, let's break down the information provided and derive the equations step by step.
### Information Provided:
1. On your first trip to the grocery store, you purchased:
- 12 pounds of sugar
- 15 pounds of flour
- Total cost: \[tex]$9.30
2. On your second trip to the grocery store, you purchased:
- 4 pounds of sugar
- 10 pounds of flour
- Total cost: \$[/tex]4.60
### Define Variables:
- Let [tex]\( s \)[/tex] represent the cost per pound of sugar.
- Let [tex]\( f \)[/tex] represent the cost per pound of flour.
### Create Equations:
1. For the first trip:
- The cost of 12 pounds of sugar: [tex]\( 12s \)[/tex]
- The cost of 15 pounds of flour: [tex]\( 15f \)[/tex]
- The total cost of the first trip: [tex]\( 12s + 15f = 9.30 \)[/tex]
2. For the second trip:
- The cost of 4 pounds of sugar: [tex]\( 4s \)[/tex]
- The cost of 10 pounds of flour: [tex]\( 10f \)[/tex]
- The total cost of the second trip: [tex]\( 4s + 10f = 4.60 \)[/tex]
### System of Equations:
Combining the above equations, we get the following system of equations:
[tex]\[
\begin{aligned}
1.\quad & 12s + 15f = 9.30 \\
2.\quad & 4s + 10f = 4.60
\end{aligned}
\][/tex]
So, the correct system of equations that represent this problem is:
[tex]\[
\begin{array}{l}
12s + 15f = 9.30 \\
4s + 10f = 4.60
\end{array}
\][/tex]
Among the provided options, matches the following:
- [tex]\( 12s + 15f = 9.30 \)[/tex]
- [tex]\( 4s + 10f = 4.60 \)[/tex]
These are represented correctly as:
[tex]\[
12s + 15f = 9.30 \\
4s + 10f = 4.60
\][/tex]
This is the correct answer.
