First solution:

Let's assume that item value equals x. Calculate the tax only on the portion of value that exceeds $1,000, only (x – $1,000) is taxable. Express the statement in the form of an equation:
0.07*(x – $1,000) = $87.50.
x - $1,000 = $1,250
x = $2,250

Second solution:

The value of the taxable portion of the item is
$ = $1,250. The total value of the item is $1,000 more: $1,250 + $1,000 = $2,250.

Third solution:

The problem can be backsolved:
A) 0.07*(1600 - 1000) = $42.00;
B) 0.07*(1850 - 1000) = $59.50;
C) 0.07*(2250 - 1000) = $87.50 - correct;
D) 0.07*(2400 - 1000) = $98;
E) 0.07*(2750 - 1000) = $122.5;

Strategy:

Substituting the statement by one or two equations is a simple and efficient way to find the answer.

Useful formulas:

Solving linear equation.