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18 February, 11:39

A customer buys five cans of baked beans, four packets of brown sugar and two packets of biscuits from a supermarket. He gives the cashier R150.00 and gets R26.00 in change. A can of baked beans costs half as much as a packet of biscuits whilst a packet of sugar is R3.00 cheaper than a packet of biscuits.

1. How much did all the items cost?

2. Calculate the cost of a can of baked beans, a packet of sugar and a packet of biscuits.

3. How much will 8 cans of baked beans, 1 packet of sugar and 6 packets of biscuits cost?

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Answers (1)
  1. 18 February, 13:05
    0
    Can of baked beans = x

    packet of brown sugar = y

    packet of biscuit = z

    5x + 4y + 2z = 150 - 26 ⇒ 5x + 4y + 2z = 124 is the total cost of all items.

    can of baked beans = x = 1/2 of z

    packet of sugar = y = z - 3

    5 (z/2) + 4 (z-3) + 2z = 124

    5z/2 + 4z - 12 + 2z = 124

    5z/2 + 6z = 124 + 12

    2 (5z/2 + 6z) = 2 (136)

    5z + 12z = 272

    17z = 272

    z = 16 cost of a packet of biscuit.

    x = 1/2 of z = 16/2 = 8 cost of a can of baked beans

    y = z - 3 = 16 - 3 = 13 cost of a packet of sugar

    5x + 4y + 2z = 124

    5 (8) + 4 (13) + 2 (16) = 124

    40 + 52 + 32 = 124

    124 = 124

    8 (8) + 1 (13) + 6 (16) = 64 + 13 + 96 = 173 total cost on question 3.
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