Nan Hua Primary School PSLE Math Prelim 2006 (Q44)

A box containing 3 files weighed 10.2 kg. Peter added 2 more files and 3 books into the box and the mass of the box with its contents became 19 kg. If the mass of one file was four times the mass of the book,

a) Find the mass of the box.
b) Peter could only lift a maximum mass of 13 kg. What was the least number of files that he could remove from the box so that he was able to lift the box?


Solution

Mass of 1 file was four times mass of the book.

File ----- 4 units
Book ----- 1 unit


Box with 3 files weighed 10.2 kg

Box + (3 x 4 units) ----- 10.2 kg

Box + 12 units ----- 10.2 kg



Peter added 2 files and 3 books, mass now 19 kg.

Box + 5 files + 3 books ----- 19 kg

Box + (5 x 4 units) + 3 units ----- 19 kg

Box + 20 units + 3 units ----- 19 kg

Box + 23 units ----- 19 kg


In summary,

Box + 12 units ----- 10.2 kg
Box + 23 units ----- 19 kg

Box with 23 units is heavier than Box with 12 units by, 19 kg – 10.2 kg = 8.8kg

This 8.8 kg is caused by the extra 11 units in Box with 23 units, as compared to Box with 12 units.

Therefore,

11 units ----- 8.8 kg

1 unit ----- 8.8 kg divided by 11 = 0.8 kg


Q(a) Mass of box is

Box + 12 units ----- 10.2 kg

Box + (12 x 0.8kg) ----- 10.2 kg

Box + 9.6 kg ----- 10.2 kg

Box ----- 10.2 kg – 9.6 kg = 0.6 kg

Answer: The box weighed 0.6 kg.


Q(b) Least number of files

1 file ---- 4 units x 0.8 kg = 3.2 kg.

If he removed 1 file, the total mass would be

19 kg – 3.2 kg = 15.8 kg


If he removed 2 files, the total mass would be

19 kg – 3.2 kg – 3.2 kg = 11.6 kg.

11.6 kg is less than 13 kg, but 15.8 kg is more than 13 kg.


Answer: Peter needed to remove 2 files so that he was able to lift the box.