Exam 1

1. Question

Given the following information:

 $+$ $+$ = $909$ $+$ $+$ = $516$ $+$ $+$ = $921$

Compute:

 $+$ $+$ = $\text{?}$

1. $434$
2. $378$
3. $921$
4. $678$
5. $528$

Solution

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:

 $+$ $+$ = $x_1$ $+$ $x_2$ $+$ $x_3$ = $41$ $+$ $53$ $+$ $434$ = $528$

1. False
2. False
3. False
4. False
5. True