The post office is selling 7 cent stamps and 9 cent stamps. If a package requires 51 cents to mail, how many 7 cent stamps are needed?
Let's assume that x represents the number of 7 cent stamps that are needed.
Since each 7 cent stamp is worth 7 cents, x 7 cent stamps is worth 7x cents.
The remaining amount needed to make 51 cents is 51 - 7x cents.
Since each 9 cent stamp is worth 9 cents, (51 - 7x) / 9 9 cent stamps are worth (51 - 7x) / 9 cents.
Because both types of stamps must add up to make 51 cents, the total value of both types of stamps is 51.
Therefore, the equation is created: 7x + 9((51 - 7x) / 9) = 51.
Simplifying the equation, we get 7x + 51 - 7x = 51.
Combining like terms, we get 51 = 51.
Since the equation is true, we know that any value of x works.
Therefore, any number of 7 cent stamps can be used to make up the 51 cents, as long as the total value of all the stamps is 51 cents.