3. Tiana placed two orders for flowers and bushes. The first order was for 24 flowers and 6 bushes. The total of the first order was \( \$ 144 \). The second order was for 18 flowers and 3 bushes. The total of the second order was \( \$ 90 \). What is the cost of each plant?

To find the cost of each plant, we need to determine the cost of a flower and the cost of a bush. Let's denote the cost of a flower as \( F \) and the cost of a bush as \( B \). From the first order, we have: \[ 24F + 6B = 144 \] From the second order, we have: \[ 18F + 3B = 90 \] We can solve this system of equations to find the values of \( F \) and \( B \). Let's solve the system of equations. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}24F+6B=144\\18F+3B=90\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}B=24-4F\\18F+3B=90\end{array}\right.\) - step2: Substitute the value of \(B:\) \(18F+3\left(24-4F\right)=90\) - step3: Simplify: \(6F+72=90\) - step4: Move the constant to the right side: \(6F=90-72\) - step5: Subtract the numbers: \(6F=18\) - step6: Divide both sides: \(\frac{6F}{6}=\frac{18}{6}\) - step7: Divide the numbers: \(F=3\) - step8: Substitute the value of \(F:\) \(B=24-4\times 3\) - step9: Calculate: \(B=12\) - step10: Calculate: \(\left\{ \begin{array}{l}B=12\\F=3\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}B=12\\F=3\end{array}\right.\) - step12: Rewrite: \(\left(B,F\right) = \left(12,3\right)\) The solution to the system of equations is \( B = 12 \) and \( F = 3 \). Therefore, the cost of each flower is \( \$3 \) and the cost of each bush is \( \$12 \).