Question

Miss has a sheet of wrapping paper 85cm in length and 60 cm in width. She cuts the paper into rectangular pieces of length 20 cm and width 10 cm to wrap a gift.

(a) what is the greatest number of pieces that can be cut from the sheet of paper?
(b) Miss wants to wrap 100 gifts. How many sheets of wrapping paper will she need?

Answer 1

Part a - 25 pieces

Part b - 4 sheets

Explanation:

Part a

Think of this in terms of how many "units" can the total paper be cut into. Easiest way to keep track of units is by their area. In other words, take the total area and see how many unit areas fit into it:

Number of units = total area / unit area

N = (85 x 60) / (20 x 10)

N = 5100 / 200

N = 25.5

Therefore the greatest number of pieces the paper can be cut into is 25 units (the 0.5 doesn't count since it's not a full pieces).

Part b

Again, back to units. This time the "total" is 100, and our unit size is 25.5. So:

Number of units = total gifts / gifts per unit

N = 100 / 25.5

N = 3.9

Therefore 4 sheets of wrapping paper will be needed (you need to round the 3.9 up because wrapping paper sheets only come in whole numbers for the purposes of this question).