4) Five pounds of fruit and 3 pounds of nuts cost \( \$ 78.66 \). Three pounds of fru and 5 pounds of nuts cost \( \$ 56.86 \). Mrs. Silvers paid \( \$ \) for 2 pound of fruit and 2 pounds of nuts.

Let's denote the cost of 1 pound of fruit as \( f \) dollars and the cost of 1 pound of nuts as \( n \) dollars. From the given information: 1. 5 pounds of fruit and 3 pounds of nuts cost $78.66: \[ 5f + 3n = 78.66 \] 2. 3 pounds of fruit and 5 pounds of nuts cost $56.86: \[ 3f + 5n = 56.86 \] We also know that Mrs. Silvers paid $ for 2 pounds of fruit and 2 pounds of nuts: \[ 2f + 2n = ? \] We need to find the value of \( 2f + 2n \) in dollars. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5f+3n=78.66\\3f+5n=56.86\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}f=\frac{3933}{250}-\frac{3}{5}n\\3f+5n=56.86\end{array}\right.\) - step2: Substitute the value of \(f:\) \(3\left(\frac{3933}{250}-\frac{3}{5}n\right)+5n=56.86\) - step3: Simplify: \(\frac{11799}{250}+\frac{16}{5}n=56.86\) - step4: Move the constant to the right side: \(\frac{16}{5}n=56.86-\frac{11799}{250}\) - step5: Subtract the terms: \(\frac{16}{5}n=\frac{1208}{125}\) - step6: Multiply by the reciprocal: \(\frac{16}{5}n\times \frac{5}{16}=\frac{1208}{125}\times \frac{5}{16}\) - step7: Multiply: \(n=\frac{151}{50}\) - step8: Substitute the value of \(n:\) \(f=\frac{3933}{250}-\frac{3}{5}\times \frac{151}{50}\) - step9: Simplify: \(f=\frac{348}{25}\) - step10: Calculate: \(\left\{ \begin{array}{l}f=\frac{348}{25}\\n=\frac{151}{50}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}f=\frac{348}{25}\\n=\frac{151}{50}\end{array}\right.\) - step12: Rewrite: \(\left(f,n\right) = \left(\frac{348}{25},\frac{151}{50}\right)\) The solution to the system of equations is: \[ f = 13.92, \quad n = 3.02 \] Now, we can calculate the cost of 2 pounds of fruit and 2 pounds of nuts: \[ 2f + 2n = 2(13.92) + 2(3.02) = 27.84 + 6.04 = 33.88 \] Therefore, Mrs. Silvers paid $33.88 for 2 pounds of fruit and 2 pounds of nuts.