The average debt for juniors exceeds the debt for sophomores by
$ 458$458,
and the average debt for seniors exceeds the debt for sophomores by
$1165.
The combined debt for a sophomore, a junior, and a senior is
$6543.
Determine the average debt for a sophomore, a junior, and a senior.
The average debt of a sophomore is
If the three classes have debts of x,y,z then we know that
y = x+458
z = x+1165
x+y+z = 6543
Now just crank it out.
Let's assign variables to the average debt of a sophomore, junior, and senior.
Let's say the average debt of a sophomore is S.
Given that the average debt for juniors exceeds the debt for sophomores by $458, the average debt for juniors would be S + 458.
Similarly, the average debt for seniors exceeds the debt for sophomores by $1165, so the average debt for seniors would be S + 1165.
Now, we know that the combined debt for a sophomore, a junior, and a senior is $6543.
If we add up the average debts of each of them, we should get the total combined debt:
S + (S + 458) + (S + 1165) = 6543.
Simplifying the equation, we get:
3S + 1623 = 6543.
Subtracting 1623 from both sides:
3S = 4920.
Dividing both sides by 3:
S = 1640.
Therefore, the average debt for a sophomore is $1640.