#### Answer

$10x + 25y = 285$
(26, 1), (21, 3), and (16, 5) are three possible options.

#### Work Step by Step

The possible options are 10 and 25 gift cards, with a limit of 285 to spend. The intercepts have decimals, so we can't use the intercepts as possible values for the quantities of gift cards purchased.
Allow the following: y=1, y =3, and y=5
y=1
$10x + 25(1) = 285$
$10x + 25 = 285$
$10x +25 (-25)= 285 (-25)$
$10x = 260$
$10x (*1/10) = 260 (*1/10)$
$ x = 26$
y=3
$10x + 25(3) = 285$
$10x + 75 = 285$
$10x +75 (-75)= 285 (-75)$
$10x = 210$
$10x (*1/10) = 210 (*1/10)$
$ x = 21$
y=5
$10x + 25(5) = 285$
$10x + 125 = 285$
$10x +125 (-125)= 285 (-125)$
$10x = 160$
$10x (*1/10) = 160 (*1/10)$
$ x = 16$