Twice Sam's age added to half her mother's age is 48. Three times her age less one third of her mother's age is 33. How old are Sam and her mother?

Sam is 15 and her mother is 36

Step-by-step explanation:

Let Sam's age be x and her mother's age by y

We can figure out Sam and her mother's age by representing these scenarios using equations with variables and solving the system using elimination

2x+y/2=48

3x-1/3y=33

You start by making all the numbers in both the equations whole

2(2x+y/2=48)

3(3x-1/3y=33)

Becomes:

4x+y=96

9x-y=99

Add together to eliminate y

13x/13=195/13

x=15

Now that we have x we can plug the value into the x in the equations to give us the y-value

2x15+y/2=48

30+y/2=48

30+y/2-30=48-30

y/2=18

2 X y/2=18 X 2

y=36

Therefore x=15 and y=36