Devaughn's age is three times Sydney's age. The sum of their ages is 40 . What is Sydney's age?

Question

 Im lost on it.

Answer 1

The key to word (story) problems is to translate the words and phrases into concise, precise mathematical expressions, with variables and operations.

 

The problem asks you to find Sydney's age.  If possible, that should be a variable (so we don't forget to solve for it at the end).

 

Let S = Sydney's age

 

      D = Devaughn's age   [could be a variable; or you could just use 3*S]

 

Translate:

  "Devaughn's age is three times Sydney's age"      means

             D            =    3      *         S                    [note:  "is" means "="]

 

  "The sum of their ages is 40"     means

             S + D              =  40                            [note: "sum" means "+"]

 

The math is now easy:

   S  +    D    = 40                [the second equation]

   S  +  (3S)  =  40              [substitute 3S from first equation for D]

 

      4S = 40                   [collect terms]

        S = 10                    [divide both sides by 4]

 

Sydney's age is 10.

 

The problem didn't ask for Devaughn's age, but it is 3*S = 30.

 

Checking:  The sum of 10 and 30 is 40.

 

[note: Good students check their work.]

Answer 2

S=Sydney's age

3S=DeVaughn's age

S+3S=40

4S=40

S=40/4

S=10 years old  (answer)