tag:blogger.com,1999:blog-2491397765324980963.post4264704998565845397..comments2021-05-07T15:18:58.771+05:30Comments on WELCOME TO THE EXCITING WORLD OF MATHEMATICS: Solve it - Question no. 18Amit Bajajhttp://www.blogger.com/profile/13191271162965966420noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2491397765324980963.post-80413257441505074832012-04-12T15:12:20.819+05:302012-04-12T15:12:20.819+05:30Posted By Prakhar Bindal (Class 8) Meerut Dewan Pu...Posted By Prakhar Bindal (Class 8) Meerut Dewan Public Schoolhhhttps://www.blogger.com/profile/08052037946468477717noreply@blogger.comtag:blogger.com,1999:blog-2491397765324980963.post-64110668319210180872012-04-12T15:11:37.838+05:302012-04-12T15:11:37.838+05:30Let the ages of the children from youngest to olde...Let the ages of the children from youngest to oldest be a; b; c; d.<br />Since the ages of the three oldest children sum to 40, b + c + d = 40. (1)<br />Since the ages of the three youngest children sum to 32, a + b + c = 32. (2)<br />Subtracting (2) from (1), we obtain d a = 8. This means that the di erence between the age<br />of the oldest child and the age of the youngest child is 8.<br />Now 17 280 = 2<br />7 3<br />3 5 = (2<br />2 3) (2<br />2 3) (2<br />2 3) 2 5 = 12 12 12 10. Since all<br />of the ages are di erent, this statement tells us that at least one child is over 12 and one child<br />is under 10.<br />There is a limited number of possibilities such that the di erence between the oldest and<br />youngest is 8 which also satisfy the condition that the youngest is under 10 and the oldest is<br />over 12. The possibilities for youngest and oldest are (5,13), (6,14), (7,15), (8,16), and (9,17).<br />No other combination would be possible since the oldest child must be over 12 and the<br />youngest child must be under 10.<br />The numbers 7, 13, and 17 are primes and are not factors of 17 280. Therefore we can<br />eliminate the possibilities where an age is one of 7, 13, or 17, leaving (6,14) and (8,16). But 14<br />contains a prime factor of 7 which is not a factor of 17 280. Since there is only one possibility<br />left, (8,16), we can conclude that the youngest is 8 and the oldest is 16.<br />Now 17 280 = 8 16 3<br />3 5. Using the remaining factors 3<br />3<br />and 5, we need to create two<br />numbers between 8 and 16. The only possibilities are 3<br />2 = 9 and 3 5 = 15.<br />Therefore the ages of the children are 8, 9, 15, and 16. It is easy to verify that this is the<br />correct solution.hhhttps://www.blogger.com/profile/08052037946468477717noreply@blogger.com