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?

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.