Twins Diana, and Riana are each 6 years older than their younger brother Kyle. Together, their three ages total 21 years. How old is kyle? Please show your work to help me understand how to work the problem
2T+K=32 and K=T-6
Put that last into the first equation for K, then solve for T.
2 x + x-6 = 21
To solve this problem, we can employ a simple algebraic approach. Let's represent Kyle's age as "x."
According to the problem, both Diana and Riana are each 6 years older than Kyle. So, we can represent their ages as "x + 6" and "x + 6" respectively.
The sum of their three ages is given as 21 years. So, we can set up the equation:
x + (x + 6) + (x + 6) = 21
Now, let's simplify and solve for x:
3x + 12 = 21
Subtracting 12 from both sides:
3x = 21 - 12
3x = 9
Finally, dividing both sides by 3:
x = 9/3
x = 3
Therefore, Kyle is 3 years old.
To check our answer, we can substitute the value we found back into the original equation:
3 + (3+6) + (3+6) = 21
3 + 9 + 9 = 21
21 = 21
This confirms that our solution is correct.