Question

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?

Answer 1

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
 

Answer 2

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;
 <1> 5x+4y+2z = Amount spent = 150-26 = 124
 <2> z = 2x
 <3> 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)