Polly Dent and Pepso Dent are sisters (one dances and the other ice skates); their combined ages make up seventeen years. When Polly was as old as Pepso was when Pepso was twice as old as Polly was when when Polly was 15 years younger than Pepso will be when Pepso is twice her present age, Polly was 2 years younger than Pepso was when Pepso was 3 years older than Polly was when Polly was a third as old as Pepso was when Pepso was a year older than Polly was 7 years ago. So, how old is Pepso?

Source: J. Hunter's *Fun With Figures*, 1956

**Hint:** Somethings to think about....you know their current ages add to 17....and you8 can assume (as a start) that their ages are in whole numbers (i.e. not 5 1/3 years old!). Thus, take a guess and try to work the problem through...

Or, will algebra help...?

Or, working backwards....?

Can you tell which sister is older?

**Solution Commentary:** All I will tell you is that one sister is 8 years old and the other is 9 years old. Can you determine which is Pepso from that start?