Answer
Scores: 526, 527, and 528.
Work Step by Step
The first integer is represented by $x$.
Second integer = $(x+1)$.
Third integer = $(x+2)$.
The sum of the first, second, and 3 times the third integers = $2637$.
Rewritten: $x+(x+1)+3(x+2) = 2637$
Simplify: $x+x+1+3x+6 = 2637$
Simplify: $5x+7 = 2637$
Isolate $x$: $\frac{5x+7 = 2637}{-7}$ -> $\frac{5x=2630}{5}$
Solve for $x$: $x = 526$.
Plug $x$ back into the integers: $(526), (526+1), (526+2)$
The scores are: $526, 527, 528$.
