A man is 4-times as old as her daughter. After 16-years, he will be twice as old as his daughter. Find the daughter’s age.

x = daughter's age now

4x = man's age now {man is 4 times as old as daughter}

x + 16 = daughter in 16 years

4x + 16 = man in 16 years

4x + 16 = 2(x + 16) {after 16 years, he will be twice as old as her}

4x + 16 = 2x + 32 {used distributive property}

4x = 2x + 16 {subtracted 16 from both sides}

2x = 16 {subtracted 2x from both sides}

x = 8 {divided both sides by 2}

4x = 32 {substituted 8, in for x, into 4x}

x = 8 {divided both sides by 4}

4x = man's age now {man is 4 times as old as daughter}

x + 16 = daughter in 16 years

4x + 16 = man in 16 years

4x + 16 = 2(x + 16) {after 16 years, he will be twice as old as her}

4x + 16 = 2x + 32 {used distributive property}

4x = 2x + 16 {subtracted 16 from both sides}

2x = 16 {subtracted 2x from both sides}

x = 8 {divided both sides by 2}

4x = 32 {substituted 8, in for x, into 4x}

x = 8 {divided both sides by 4}

**daughter is 8***- Algebra House*