Question

Sandra bought 4 bars of chocolate and a packet of nuts for $11.50. If a bar of chocolate costs $0.50 less than a packet of nuts, find the cost of a packet of nuts

Answer 1

Answer:

A packet of nuts costs $2.70

Step-by-step explanation:

Let C represent the cost of a bar of chocolate and P represent the cost of a packet of nuts

4 bars of chocolate will cost $4C

1 packet of nuts costs $P

Total price Sandra paid is $11.50

This can be represented using

4C + P = 11.50    (1)

A bar of chocolate costs $0.50 less than a packet of nuts. So

P - C =0.50  

-C + P = 0.50   (2)

Multiply eq (2) by 4 to get

-4C + 4P = 4 x 0.50

-4C + 4P = 2   (3)

Add equations (1) and (3) to eliminate the 4C term

4C + P - 4C + 4P = 11.50 + 2

P+4P = 13.50

5P = 13.50

Dividing by 5 on both sides

5P/5 = 13.50/5

P = 2.70

So a packet of nuts costs $2.70  (Answer)

To verify this is correct,

Use equation (2) to get

-C + P = 0.50

-C + 2.70 = 0.50

Add C to both sides

-C + 2.70 + C = 0.50 + C

2.70 = 0.50 + C

Subtract 0.50 from both sides

2.70-0.50 = 0.50 + C - 0.50

2.20 = C which is C= 2.20

Plug this value into equation (1)

4(2.20) + 2.70 = 8.80 + 2.70 = 11.50

So verified that answers are correct