   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: Hello: 2/3 of Mary's age equals Sarah's age and 3/4 of Ruth's age equals Sarah's age. If the total ages equal 46, how old is each girl? Answer: Mary 18, Ruth 16, Sarah 12 Solution: 3/2 of Sarah's age equals Mary's age. 4/3 of Sarah's age equals Ruth's age. 6/6 of Sarah's age equals Sarah's age. 46 divided by 23/6 equals Sarah's age of 12. Can the following similar situation be solved if the two girls ages do not equal Sarah's age? 2/3 of Mary's age equals Ruth's age and 3/4 of Ruth's age equals Sarah's age. How old is each girl? Their ages may not be the same as those in the above example. I thank you for your reply. Kenneth,

"2/3 of Mary’s age equals Ruth’s age'': You multiply by 3/4:
"3/4 x (2/3 of Mary’s age) equals 3/4 x (Ruth’s age)''.
Then use 3/4 x 2/3 = 1/2, and 3/4 x Ruth's age = Sarah's age:
"1/2 of Mary’s age equals Sarah’s age''.

Claude     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.