Given the following information:
$+$ | $+$ | = | $909$ | |||
$+$ | $+$ | = | $516$ | |||
$+$ | $+$ | = | $921$ |
Compute:
$+$ | $+$ | = | $\text{?}$ |
The information provided can be interpreted as the price for three fruit baskets with different combinations of the three fruits. This corresponds to a system of linear equations where the price of the three fruits is the vector of unknowns $x$:
$x_1 =$ | $x_2 =$ | $x_3 =$ |
The system of linear equations is then: $\begin{aligned} \left( \begin{array}{rrr} 1 & 0 & 2 \\ 2 & 0 & 1 \\ 0 & 1 & 2 \end{array} \right) \cdot \left( \begin{array}{r} x_1 \\ x_2 \\ x_3 \end{array} \right) & = & \left( \begin{array}{r} 909 \\ 516 \\ 921 \end{array} \right) \end{aligned}$ This can be solved using any solution algorithm, e.g., elimination: $x_1 = 41, \, x_2 = 53, \, x_3 = 434.$ Based on the three prices for the different fruits it is straightforward to compute the total price of the fourth fruit basket via:
$+$ | $+$ | = | ||||
$x_1$ | $+$ | $x_2$ | $+$ | $x_3$ | = | |
$41$ | $+$ | $53$ | $+$ | $434$ | = | $528$ |