Tamara has two sisters. One of her sister is 7 years older than Tamara. The other is 3 years younger than Tamara. The prosuct of Tamara's sister's age is 24. How oold is Tamara?
Let's assume Tamara's age is "x" years.
According to the information given, one of her sisters is 7 years older than Tamara. So, her sister's age would be x + 7 years.
The other sister is 3 years younger than Tamara, so her age would be x - 3 years.
The product of Tamara's sisters' ages is 24, so we can create the equation:
(x + 7) * (x - 3) = 24
Now, let's solve this equation step-by-step:
Expanding the equation:
x^2 - 3x + 7x - 21 = 24
Combining like terms:
x^2 + 4x - 21 = 24
Rearranging the equation:
x^2 + 4x - 45 = 0
Factoring the equation:
(x + 9)(x - 5) = 0
Setting each factor equal to zero:
x + 9 = 0 or x - 5 = 0
Solving for x:
If x + 9 = 0, then x = -9
If x - 5 = 0, then x = 5
Since age cannot be negative, we can eliminate x = -9 as a valid solution.
Therefore, Tamara is 5 years old.
To find Tamara's age, we need to analyze the given information and use the clues provided.
Let's assume Tamara's age is "T."
We know that one of Tamara's sisters is 7 years older than her. So, that sister's age would be T + 7.
The other sister is 3 years younger than Tamara. So, her age would be T - 3.
According to the problem statement, the product of Tamara's sister's ages is 24, which means (T + 7) * (T - 3) = 24.
Expanding the equation, we have T^2 + 4T - 21 = 0.
Now, we can solve this quadratic equation by factoring or by using the quadratic formula.
By factoring, we look for two numbers that multiply to -21 and add up to +4. The numbers that satisfy this condition are +7 and -3.
So, factoring the quadratic equation, we have (T + 7)(T - 3) = 0.
Setting each factor equal to zero, we get T + 7 = 0 or T - 3 = 0.
For T + 7 = 0, subtracting 7 from both sides gives us T = -7, which doesn't make sense in the context of the problem.
For T - 3 = 0, adding 3 to both sides gives us T = 3.
Therefore, Tamara's age is 3 years old.
Let x = Tamara's age.
One sister is x + 7, while the other is x -3.
(x + 7)(x - 3) = 24
Solve for x.
I hope this helps. Thanks for asking.
P.S. Watch out for the typos. They didn't effect this message, but they are likely to effect future ones. DAG