Annie's older sister Beth is 3 years older then her and Annie's mom is 3 times older then her and all there ages add up to 63 how old is each person

Question

Annie's sister Beth is 3 years older then her Annie's mom is 3 times older then Annie all of there ages add up to 63 how old is each one---------------------------------------------

Answer 1

3 equations, 3 unknowns, should be doable!

 

A = Annie's age

B = Beth's age

M = Mom's age

 

• B=A+3 (sister is 3 years older than Annie)
• M=3A (Mom is 3 times as old as Annie)
• A+B+M=63 (all their ages add to 63)

 

The first two equations are already in terms of A, so we can just plug those into the third equation.

 

A+(A+3)+3A=63

5A+3=63

5A=60

A=12

 

So Annie is 12, then Beth is 15 (12+3) and Mom is 36 (12*3).  

 

A quick check gives 12+15+36=63

Answer 2

Hi Alex,

 

There are three people here:

Annie

Beth

Mom

 

Let Annie's age equal x because Annie's age determines Beth's. (Annie = x)

Let Beth's age equal x + 3 because Beth is 3 years older. (Beth = x + 3)

Let Mom's age equal 3x since mom is three times as old as Annie. (Mom = 3x).

 

Altogether, the three equal 63.

 

x + x + 3 + 3x = 63

Combine the x terms.

 

            5x + 3 = 63

Subtract both sides by 3.

    

 

             5x = 60

Now divide both sides by 5 to isolate x.

 

               x = 12.

 

Annie is 12 years old, Beth is x + 3 or 15 years old, and Mom is 12(3) or 36 years old.