age difference word problem

Question

Mark is 3 years older than Christy, and the sum of their ages is 16. How old are mark and christy?

Answer 1

Let Mark's age is x and Christy's age is y then

 

x=y+3 ...Eq1    and the sum of their age is 16 so we also have,

 

x+y=16...Eq2

 

Let us substitute x=y+3 in Eq2 and so we will now have,

 

(y+3)+y=16

 

∴2y+3=16

∴2y=16-3

∴2y=13

∴y=13/2=6 1/2

Here 1 year is 12 months and hence 1/2 is 6 months.

So y=6 years and 6 months.

 

put this value in Eq1

∴x=y+3

     =6  1/2+3

     =19/2

     =9 1/2

     =9 years and 6 months

 

So Marks' age is 6 years and 6 months and

Christy's age is 9 years and 6 months.......Ans

 

 

Lets check if they adds upto 16

6 1/2+9 1/2=13/2+19/2=32/2=16 years.

Answer 2

Ma,

Mark is m years old

Christy is c years old

"Mark is 3 years older" means m=c+3

"sum of their ages is 16" means c+m=16 but m=c+3

So, c+c+3=16

2c+3-3=16-3

2c=13

c=6½ and m=9½