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}

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 nowBill is 35 now

*- Algebra House*