# What would be the equation to express Sarah's age if Sarah is 24 years younger than her mother and if the sum of their ages is 68?

Aug 5, 2018

color(purple)(x + (x +24) = 68, color(magenta)(" where 'x' is Sara's age"

color(chocolate)("Sara's Age " = x = 22 " years"

#### Explanation:

$\text{Let Sara's age be } \textcolor{c r i m s o n}{x}$

$\text{Age of Sara's mother } = x + 24$

$\therefore x + \left(x + 24\right) = 68$

$2 x = 68 - 24 = 44$

color(brown)("Sara's Age " x = 44/2 = 22 " years"

Aug 5, 2018

$2 S + 24 = 68$ or

S = 22

#### Explanation:

let S = Sarah's age
Let M = Mother's age

S + M = 68
S + 24 = M

combining the two equations putting S + 24 for M gives

S + S + 24 = 68

Add the 2 S's and subtract the 24 from both sides

$S + S + 24 - 24 = 68 - 24$

This gives

$2 S = 44$

divide both sides by 2

$2 \frac{S}{2} = \frac{44}{2}$

S = 22