Tom is 6 times as old as Todd. In 5 years Tom's age will be 31 years more than 2 times as old as Todd. How old is Tom?

x = Todd's age now

6x + 5 = 2(x + 5) + 31 {in 5 years, Tom will be 31 more than 2 times Todd}

6x + 5 = 2x + 10 + 31 {used distributive property}

4x + 5 = 2x + 41 {combined like terms}

4x = 36 {subtracted 2x and 5 from each side}

x = 9 {divided each side by 2}

6x = 54 {substituted 13, in for x, into 6x}

**6x = Tom's age now**{Tom is 6 times as old as Todd}**x + 5 = Todd's age in 5 years**{added 5 onto current age}**6x + 5 = Tom's age in 5 years**{added 5 onto current age}6x + 5 = 2(x + 5) + 31 {in 5 years, Tom will be 31 more than 2 times Todd}

6x + 5 = 2x + 10 + 31 {used distributive property}

4x + 5 = 2x + 41 {combined like terms}

4x = 36 {subtracted 2x and 5 from each side}

x = 9 {divided each side by 2}

6x = 54 {substituted 13, in for x, into 6x}

**Tom is 54***- Algebra House*