Alvita is planning a garden patio to be made from identical square paving stones laid out in a rectangle measuring 2 stones by y stones.
She finds that when she adds a border of width one stone around the patio, the area of the border is equal
to the original area of the patio.
How many possible values for x are there?

Step-by-step explanation:

what means "x" ?

anyway, we have an original rectangle

2 stones × y stones with the area of 2y.

adding a border of one line of stones around that requires

3 stones on both sides (2 stones next to the existing ones, and 1 stone for the extra row above the existing 2 rows) and another row of y stones.

that are 2×3 + y = 6 + y stones.

the area of a 1 stone thick border is exactly also the number of used stones = 6 + y.

and now we know that the original area (2y) is the same as the area of the new border.

so,

2y = 6 + y

y = 6

there is only one possible solution, as this is a linear equation (polynomial of first or 1 degree).

coins of silver or gold

step-by-step explanation: