Answer: (#22) 11 years old
Explanation:
The total ages of three students is 34. If the youngest student is 9 years younger than the oldest student, and the middle student is 4 years older than the youngest student, how old is the middle student?
Ok let's call the students' ages a, b, and c. (a is the youngest, b is the middle, c is the oldest.) The problem tells us that
a + b + c = 34,
a = c - 9, and
b = a + 4.
We want to transform the first equation into just b's, because then we can solve for b and get the middle student's age. We're going to do this using substitution. So from the third equation, rearranging it yields a = b - 4, so now we substitute that for a in the first equation:
(b - 4) + b + c = 34.
Now we need to turn the c into something with b's. Well the second equation tells us a = c - 9, so c = a + 9. What now? Well maybe we could substitute b-4 for a in this equation to get
c = (b - 4) + 9
which means c = b + 5. So now we can substitute that to get
(b - 4) + b + (b + 5) = 34
3b + 1 = 34
3b = 33
b = 11,
So the middle student's age is 11.