A factory makes chocolate bars. Five boxes, labelled , are each packed with 20 bars. Each of the bars in three of the boxes has a mass of 100 g. Each of the bars in the other two boxes has a mass of 90 g. One bar is taken from box , two bars are taken from box , four bars are taken from box , eight bars are taken from box , and sixteen bars are taken from box . The total mass of these bars taken from the boxes is 2920 g. Which boxes contain the 90 g bars?
Problem 493
Official solution
The number of bars taken from the boxes is . If these bars all had mass 100 g, their total mass would be 3100 g. Since their total mass is 2920 g, they are lighter. Since all of the bars have a mass of 100 g or of 90 g, then it must be the case that 18 of the bars are each 10 g lighter (that is, have a mass of 90 g). Thus, we want to write 18 as the sum of two of in order to determine the boxes from which the 90 g bars were taken. We note that and so the 90 g bars must have been taken from box and box .