Question

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**.