Age Problem with Bill and Cindy

Bill is seven times old as his niece, Cindy. Five years from now, Bill will be four times as old as Cindy will be then.  How old is Cindy now? 

---

x = Cindy's age now
7x = Bill's age now {he is seven times as old as Cindy} 

x + 5 = Cindy's age in 5 years
7x + 5 = Bill's age in 5 years 

7x + 5 = 4(x + 5) {in 5 years Bill will be 4 times as old as Cindy}
7x + 5 = 4x + 20 {used distributive property}
7x = 4x + 15 {subtracted 5 from both sides}
3x = 15 {subtracted 4x from both sides}
x = 5 {divided both sides by 3}
7x = 35 {substituted 5 in for x into 7x} 

Cindy is 5 now
Bill is 35 now


- Algebra House