Exam 1

  1. Question

    Given the following information:
    banana.png + pineapple.png + banana.png = 564
    banana.png + pineapple.png + pineapple.png = 873
    orange.png + pineapple.png + pineapple.png = 864
    Compute:
    banana.png + orange.png + pineapple.png = ?

    1. 394
    2. 555
    3. 507
    4. 873
    5. 594

    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:
    x1 = banana.png x2 = orange.png x3 = pineapple.png
    The system of linear equations is then:
    ( 201 102 012 )·( x1 x2 x3 ) = ( 564 873 864 )

    This can be solved using any solution algorithm, e.g., elimination:
    x1 =85, x2 =76, x3 =394.

    Based on the three prices for the different fruits it is straightforward to compute the total price of the fourth fruit basket via:
    banana.png + orange.png + pineapple.png =
    x1 + x2 + x3 =
    85 + 76 + 394 = 555.