Question

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?

Answer 1

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

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

Explanation:

`"Let Sara's age be " color(crimson)(x)`

`"Age of Sara's mother " = x + 24`

`:. x + (x +24) = 68`

`2x = 68 - 24 = 44`

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

Answer 2

`2S + 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

`2S = 44`

divide both sides by 2

`2S/2 = 44/2`

S = 22