Intermediate Algebra (6th Edition)

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: $526, 527, 528$.