To represent the given situation as a system of equations, we need to define the variables and then use the given prices and total costs at each store.
Let's define:
- [tex]\( x \)[/tex] as the number of loaves of bread that Sue buys.
- [tex]\( y \)[/tex] as the number of gallons of milk that Sue buys.
For Store A:
- The price of one loaf of bread is \[tex]$3.19.
- The price of one gallon of milk is \$[/tex]4.59.
- The total amount Sue would pay at Store A is \[tex]$137.24.
So, the equation for Store A would be:
\[ 3.19x + 4.59y = 137.24 \]
For Store B:
- The price of one loaf of bread is \$[/tex]3.49.
- The price of one gallon of milk is \[tex]$4.39.
- The total amount Sue would pay at Store B is \$[/tex]140.04.
So, the equation for Store B would be:
[tex]\[ 3.49x + 4.39y = 140.04 \][/tex]
Therefore, the system of equations that represents this situation is:
[tex]\[
\begin{cases}
3.19x + 4.59y = 137.24 \\
3.49x + 4.39y = 140.04
\end{cases}
\][/tex]
This system of equations correctly represents the prices and the total costs at both stores for the bread and milk that Sue wants to buy.
