1 2 3 4 5 6 7 8 9 10 A small fruit basket with 6 apples and 6 oranges costs \( \$ 7.50 \). A different fruit basket with 10 apples and 5 oranges costs \( \$ 8.75 \). If \( x \) is the cost of one apple and \( y \) is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. What is the cost of one apple? 0.25 0.5 0.75 1.00

To solve the problem, we need to set up a system of equations based on the information provided about the fruit baskets. 1. **Extract known conditions:** - The first basket has 6 apples and 6 oranges, costing \( \$7.50 \). - The second basket has 10 apples and 5 oranges, costing \( \$8.75 \). - Let \( x \) be the cost of one apple and \( y \) be the cost of one orange. 2. **Set up the equations:** From the first basket: \[ 6x + 6y = 7.50 \] From the second basket: \[ 10x + 5y = 8.75 \] 3. **Simplify the equations:** We can simplify the first equation by dividing everything by 6: \[ x + y = 1.25 \quad (1) \] For the second equation, we can simplify by dividing everything by 5: \[ 2x + y = 1.75 \quad (2) \] 4. **Solve the system of equations:** We will solve these two equations together. Now, I will use the tool to solve the system of equations. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=1.25\\2x+y=1.75\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=1.25-y\\2x+y=1.75\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\left(1.25-y\right)+y=1.75\) - step3: Simplify: \(2.5-y=1.75\) - step4: Move the constant to the right side: \(-y=1.75-2.5\) - step5: Subtract the numbers: \(-y=-0.75\) - step6: Change the signs: \(y=0.75\) - step7: Substitute the value of \(y:\) \(x=1.25-0.75\) - step8: Calculate: \(x=0.5\) - step9: Calculate: \(\left\{ \begin{array}{l}x=0.5\\y=0.75\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=0.5\\y=0.75\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(0.5,0.75\right)\) The solution to the system of equations is: \[ (x, y) = (0.5, 0.75) \] This means: - The cost of one apple \( x \) is \( 0.5 \) (or \( \$0.50 \)). - The cost of one orange \( y \) is \( 0.75 \) (or \( \$0.75 \)). Thus, the cost of one apple is \( \$0.50 \). The correct answer is **0.5**.