Quote:

$\displaystyle \text{George has a collection of old stamps.}$

$\displaystyle \text{Some are worth 29 cents, the rest are worth a quarter.}$

$\displaystyle \text{Their total value is \$5.02.}$

$\displaystyle \text{How many 29 cent stamps does George have?}$

$\displaystyle \text{Let: }\;\begin{Bmatrix}x &=& \text{number of 29-cent stamps} \\

y &=& \text{number of 25-cent stamps} \end{Bmatrix}$

$\displaystyle \text{Then: }\;29x + 25y \:=\: 502$

$\displaystyle \text{Solving for }x\!:\;\;x \:=\: \dfrac{502 - 25y}{29}$ .[1]

$\displaystyle \text{I know }x\text{ is an integer, so }502 - 25y\text{ is a multiple of 29}$

$\displaystyle \text{How would I use this knowledge to find }x\,?$