In January​ 2013, a​ country's first-class mail rates increased to 60 cents for the first​ ounce, and 15 cents for each additional ounce. If Sabrina spent ​$18.00 for a total of 51 stamps of these two​ denominations, how many stamps of each denomination did she​ buy?

Answer 1

To solve this problem, we need to define the variables and set up equations based on the information provided.

Let:

• \( x \) = number of first-ounce stamps purchased (60 cents each)
• \( y \) = number of additional-ounce stamps purchased (15 cents each)

From the problem statement, we have the following information:

1. The total number of stamps is 51.
2. The total cost of the stamps is $18.00 (or 1800 cents).

We can create two equations based on this information.

Equation 1: Total number of stamps

\[ x + y = 51 \]

Equation 2: Total cost of stamps

The cost in cents for \( x \) first-ounce stamps and \( y \) additional-ounce stamps is: \[ 60x + 15y = 1800 \]

Now we have a system of two equations:

1. \( x + y = 51 \)
2. \( 60x + 15y = 1800 \)

Next, we can solve this system using substitution or elimination. We will use substitution.

From Equation 1, we can express \( y \) in terms of \( x \): \[ y = 51 - x \]

Now we substitute \( y \) into Equation 2: \[ 60x + 15(51 - x) = 1800 \]

Expanding this gives: \[ 60x + 765 - 15x = 1800 \]

Combining like terms: \[ 45x + 765 = 1800 \]

Now, we isolate \( x \): \[ 45x = 1800 - 765 \] \[ 45x = 1035 \] \[ x = \frac{1035}{45} = 23 \]

Now that we have \( x \), we can find \( y \): \[ y = 51 - x = 51 - 23 = 28 \]

Final counts:

• \( x = 23 \) (first-ounce stamps)
• \( y = 28 \) (additional-ounce stamps)

Thus, Sabrina bought 23 first-ounce stamps and 28 additional-ounce stamps.