Question

7. A distribution centre sends three different types of parcels. One consignment has 6 small, 8 medium and 9 large parcels which cost $173. 20 to post. Another consignment has 7 small, 13 medium and 17 large parcels with total postage $291. 5. A large parcel costs twice as much to post as a small one. Work out the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels

Answer 1

Cost of posting 3 small, 9 medium and 2 large parcels = $94.45

Let the cost of a small parcel be x

Let the cost of a medium parcel be y

Let the cost of a large parcel be z

Cost of 6 small, 8 medium and 9 large parcels:

6x + 8y + 9z = 173.20------(1)

Cost of 7 small, 13 medium and 17 large parcels:

7x + 13y + 17z = 291.5-------(2)

Also, a large parcel costs twice as much as a small parcel, therefore

z = 2x

Substituting z = 2x in equation (1) and (2) we get:

24x + 8y = 173.20------(3)

41x + 13y = 291.5--------(4)

Multiplying equation (3) with 13 and equation (4) with 8 we get

312x + 104y = 2251.6

328x + 104y = 2332

By solving the equations we get

16x = 80.4

x = 5.02

Putting x = 5.02 in equation (3) we get:

y = 6.59

z = 10.04

Cost of posting 3 small, 9 medium and 2 large parcels: 3*5.02 + 9*6.59 + 2*10.04 = 15.06 + 59.31 + 20.08 = $94.45

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