A customer buys five cans of baked beans, four pocket of brown sugar and two pockets from the supermarket. He gives the cashier 150 and gets 26 in change, a can of baked beans costs half as much as pocket of biscuits whilst a packet of sugar is three rand cheaper than a packet of biscuits.

1. how much did all items cost

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

3. How much will eight cans of baked beans, one packet of sugar and six pockets of biscuits cost?

Let's make b the can of baked beans.

Then biscuits are twice its prize, 2b.

s, the packet of sugar is 2b-3 - thre rand cheaper than a packet of biscuits.

1) the custommer bought:

buys five cans of baked beans, four pocket of brown sugar and two pockets

5b+4 * (2b-3) + 2*2b

now we calculate:

5b+4 * (2b-3) + 2*2b=5b+8b-12+4b=13b-12+4b=17b-12

this is equal to 150-26=124

so 17b-12=124

17b=136

b=8

So the beans cost 8, biscuits cost 8*2=16, and sugar 16-3=13

2) this would be:

8+13+16=21+16=37

3) This would be:

8*8+13+6*16=64+13+96=173

The question has 3 unknowns thus we need three equations to fully solve the problem.

We let x = the price of a can of baked beans, y = the price of a packet of sugar and z = the price of a packet of biscuit

From the given, we generate the following equations;

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

z = 2x

y = z - 3

We use equation 2 and 3 to substitute to equation 1 in order to obtain the value of x.

5x + 4 (2x - 3) + 2 (2x) = 124

5x + 8x - 12 + 4x = 124

17x = 136

x = 8 (price of a can of baked beans)

y = (2 x 8) - 3 = 13 (price of a packet of sugar)

z = 2 x 8 = 16 (price of a pocket of biscuit)

For the new set of conditions,

8x + y + 6z = (8 x 8) + 13 + (6 x 16) = 173 (Cost for the new set of conditions)