Tiêu đề 9 Age Problem.pdf ✅

MSTC 9: Age Problems In problems where the ages of the people involved are required, the main principle is that all people age at the same rate. Say A and B are the ages of two people at year 1. At year 5, four years from now, their ages will be A + 4 and B + 4, respectively. This principle can also work retroactively for their past ages. Always remember that when there are n unknowns in a problem, n equations are required. Tables are useful when solving age problems. Person Past age k years before Present age Future age k years from now Person 1 A − k A A + k Person 2 B − k B B + k ... ... ... ... The wording in the situation is also crucial. Ages described with “was” means that it is a past age. If it is described with “is,” then it is the present age. Future ages are described with “will be.” For example, “Daniel is twice as old as James was three years ago.” Here, there are two time periods, the present and three years ago. Making a table, Person Past age 3 years before Present age Daniel D − 3 D James J − 3 J Since Daniel’s age is described as “is,” it refers to Daniel’s present age. On the other hand, James’ age referred to the problem as his past age since it is described as “was.” Making the equation from the statement, D = 2(J − 3) In some problems, the ages of a group are taken collectively instead of individually. For example, “The sum of parents’ ages is twice the sum of their children’s ages. Five years ago, the sum of the parents’ ages was four times the sum of their children’s ages. In 15 years, the sum of the parents’ ages will be equal to the sum of their children’s ages. How many children are there?” When solving problems with this case, the common approach is to take the average of the ages of the group and relate that to the averages of the others. Let the average of the parents’ ages be P, and the average of the children’s ages be C. If there are m children, their present age will be mC. Meanwhile, there are just two parents, so their ages will be 2P. Making the table for this problem, Group Past age 5 years before Present age Future age 15 years from now Parents 2(P − 5) 2P 2(P + 15) Children m(C − 5) mC m(C + 15)