Question

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?

Answer 1

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.