A gym is 21 years newer than the auditorium. The gym is also one fourth as old as the auditorium. How old is each building?
Choices for auditoriums age:26, 27, 28
Let's solve this problem step by step.
First, let's assume the age of the auditorium is "x" years.
According to the problem, the gym is 21 years newer than the auditorium. So, the age of the gym would be "x + 21" years.
Next, it says that the gym is one fourth (1/4) as old as the auditorium. So, we can set up the following equation:
age of gym = (1/4) * age of auditorium
(x + 21) = (1/4) * x
To solve for x, let's multiply both sides of the equation by 4 to eliminate the fraction:
4 * (x + 21) = x
Distribute the 4 on the left side of the equation:
4x + 84 = x
Now, subtract x from both sides:
4x - x + 84 = 0
Combine like terms:
3x + 84 = 0
Subtract 84 from both sides:
3x = -84
Finally, divide both sides by 3 to solve for x:
x = -84 / 3
The result is x = -28.
Since the age of a building cannot be negative, we can conclude that the auditorium is 28 years old, and the gym would be 28 + 21 = 49 years old.
So, the answer is:
- Auditorium: 28 years old
- Gym: 49 years old
gymage +21=audage
gymage=audage/4
audage/4+21=audage
21=3/4 aud age
aud age=you do it.