Answer :
Answer:
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
Final answer:
To solve the problem, linear equations representing the relationships between Sam's age and her mother's age are formed and solved, revealing that Sam is 15 years old and her mother is 36 years old.
Explanation:
The question involves solving a system of linear equations to find the ages of Sam and her mother. Let's denote Sam's age as S and her mother's age as M. The given conditions are:
- Twice Sam's age added to half her mother's age is 48.
- Three times Sam's age less one third of her mother's age is 33.
These conditions can be translated into the following equations:
- 2S + 0.5M = 48
- 3S - (1/3)M = 33
To solve these equations, we can first multiply both equations by a common factor to eliminate the fractions. Multiplying the first equation by 2 and the second by 3 gives us:
- 4S + M = 96
- 9S - M = 99
Adding both equations, we get 13S = 195, so Sam's age S = 15. Substituting S = 15 in the first original equation: 2(15) + 0.5M = 48, we find that M, or the mother's age, is 36.
