Question

Joe spent $15.75 on 21 pieces of fruit to make a salad. Bananas cost $.50 each, oranges cost $.075 each, and papayas cost $1.25 each. Joe used twice as many oranges as bananas. How many of each fruit did he buy?

Answer 1

$x - bananas\\ y - oranges\\ z - papayas\\$

$\begin{cases} x + y + z = 21\\ 0.5x + 0.75y + 1.25z = 15.75\\ y = 2x \end{cases}$ $\begin{cases} x + 2x + z = 21\\ 0.5x + 0.75\cdot2x + 1.25z = 15.75\\ y = 2x \end{cases}$

$\begin{cases} 3x + z = 21\\ 2x + 1.25z = 15.75\\ y = 2x \end{cases}\\$ $\begin{cases} z = 21 - 3x\\ 2x + 1.25z = 15.75\\ y = 2x \end{cases}$ $\begin{cases} z = 21 - 3x\\ 2x + 1.25\cdot(21 - 3x) = 15.75\\ y = 2x \end{cases} \begin{cases} z = 21 - 3x\\ 2x + 26.25 - 3.75x = 15.75\\ y = 2x \end{cases} \begin{cases} z = 21 - 3x\\ -1.75x = 15.75 - 26.25\\ y = 2x \end{cases}\\ \begin{cases} z = 21 - 3x\\ 1.75x = 10.5\\ y = 2x \end{cases} \begin{cases} z = 21 - 3x\\ x = 6\\ y = 2x \end{cases} \begin{cases} z = 21 - 18\\ x = 6\\ y = 12 \end{cases} \begin{cases} z = 3\\ x = 6\\ y = 12 \end{cases}\\\\$

Answer: 6 bananas, 12 oranges, 3 papayas