Tammy is 2 years older than twice the age of her brother. The sum of their ages is 17.
If x represents the age of her brother, which equation represents this situation?
2 x + 2 = 17
2( x + 2) = 17
x + 2( x + 2) = 17
x + (2 x + 2) = 17
To find the equation that represents this situation, we need to break down the information given.
Let x represent the age of Tammy's brother.
The first piece of information states that Tammy is 2 years older than twice the age of her brother. This can be written as:
Tammy's age = 2 * (Tammy's brother's age) + 2
The second piece of information states that the sum of their ages is 17. This can be written as:
Tammy's age + Tammy's brother's age = 17
Now we can substitute the first equation into the second equation:
(2 * (Tammy's brother's age) + 2) + Tammy's brother's age = 17
Simplifying this equation, we have:
2 * Tammy's brother's age + 2 + Tammy's brother's age = 17
Combining like terms:
3 * Tammy's brother's age + 2 = 17
Subtracting 2 from both sides:
3 * Tammy's brother's age = 15
Dividing both sides by 3:
Tammy's brother's age = 5
Now we substitute this value back into the first equation to find Tammy's age:
Tammy's age = 2 * (5) + 2
Tammy's age = 10 + 2
Tammy's age = 12
So, Tammy's age is 12 and her brother's age is 5.
To find the equation that represents this situation, we need to rewrite the equation in terms of x (Tammy's brother's age). Let's examine the answer choices:
A) 2 x + 2 = 17
This equation does not match the information given. It only represents Tammy's age in terms of her brother's age, without taking into account the 2-year age difference.
B) 2( x + 2) = 17
This equation represents Tammy's age in terms of her brother's age, with the correct 2-year age difference included. However, it does not represent the sum of their ages.
C) x + 2( x + 2) = 17
This equation represents both Tammy's age and her brother's age, with the correct 2-year age difference included. However, it does not represent the sum of their ages.
D) x + (2 x + 2) = 17
This equation represents both Tammy's age and her brother's age, with the correct 2-year age difference as well as the sum of their ages. Therefore, the correct equation that represents this situation is D) x + (2 x + 2) = 17.