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

Given:
Let baked beans be x
Let brown sugar be y
Let biscuits be z

5x + 4y + 2z = 150 - 26
5x + 4y + 2z = 124

a can of baked beens costs half as much as a packet of biscuits: 
x = 1/2 * z = z/2

a packet of sugar is 3.00 cheaper than a packet of biscuits
y = z - 3

We substitute x and y with its values:

5x + 4y + 2z = 124 ; x = z/2 ; 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 = 272/17
z = 16  price of a packet of biscuits.

can of baked beans : x = z/2 ; x = 16/2 = 8
packet of sugar : y = z - 3 ; y = 16 - 3 = 13

5x + 4y + 2z = 124
5(8) + 4(13) + 2(16) = 124
40 + 52 + 32 = 124
124 = 124