Question

Define your variable, set up an equation, solve the equation, state your solution in a sentence.

5) A stamp collection of 53 stamps has a total value of $10.30. The collection consists of 5¢ stamps, 10¢
stamps, and 25 stamps. The number of 25° stamps is four times the number of 10¢ stamps. Find the
number of 5¢ stamps in the collection.

Answer 1

To find the number of 5¢ stamps in the collection, we can set up an equation using the information given and solve for the variable x. The solution is x = 5, which means there are 5 5¢ stamps in the collection.

Step-by-step explanation:

Let x be the number of 5¢ stamps.

Since the number of 25¢ stamps is four times the number of 10¢ stamps, we can say that the number of 25¢ stamps is 4x.

The total number of stamps in the collection is x + 4x + x = 6x.

The total value of the stamps is $10.30, which is equivalent to 1030 cents.

Since each 5¢ stamp is worth 5 cents, each 10¢ stamp is worth 10 cents, and each 25¢ stamp is worth 25 cents, we can create the equation: 5x + 10(4x) + 25(6x) = 1030.

By simplifying the equation, we get 5x + 40x + 150x = 1030.

Combining like terms, we have 195x = 1030.

Dividing both sides of the equation by 195, we find that x = 5.28.

Since the number of stamps must be a whole number, we round x down to 5.

Therefore, there are 5 5¢ stamps in the collection.