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Question 1202434: Tim and Tala are brother and sister. Their ages total 36. The difference between twice Tala's age and Tim's age is 12. Find their ages.
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52876)   (Show Source):
You can put this solution on YOUR website! .
Tim and Tala are brother and sister. Their ages total 36.
The difference between twice Tala's age and Tim's age is 12. Find their ages.
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x = Tim's age; y = Tala's age.
Equations
2y - x = 12
y + x = 36.
Add equations
3y = 12 + 36 = 48 ---> y = 48/3 = 16.
Tala is 16 years old.
Tim is 36 - 16 = 20 years old.
Solved.
Answer by josgarithmetic(39630)  (Show Source):
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Note that you have received two earlier responses, one showing a single solution and another showing two solutions.
If we want to be mathematically correct, there is only the one solution. The second solution is possible only if we don't follow strict mathematical rules.
In everyday English usage, the difference between 5 and 3 is 2, and the difference between 3 and 5 is 2. The order is not important; the difference is always considered to be positive (or non-negative).
However, in mathematics, the order is important. The difference between a and b is always a-b; it is never b-a. So in mathematics the difference between 5 and 3 is 2, but the difference between 3 and 5 is -2.
So in your problem, if x is Tim's age and y is Tala's age, then the difference between twice Tala's age and Tim's age is 2y-x. That leads to the single mathematically correct solution to the problem:
x + y = 36
2y - x = 12
3y = 48
y = 16
x = 36-16 = 20
ANSWER: Tim 20, Tala 16
With that solution, the difference between twice Tala's age and Tim's age is 12, as it needs to be: 2(16)-20 = 32-20 = 12.
To get the second, mathematically incorrect, answer, we need to have the difference between twice Tala's age and Tim's age in the wrong order:
x + y = 36
x - 2y = 12
3y = 24
y = 8
x = 36-8 = 28
mathematically incorrect answer: Tim 28, Tala 8
With this incorrect solution, the difference between twice Tala's age and Tim's age is NOT 12: 2(8)-28 = 16-28 = -12.
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