Question

Liv bought 50 stamps some costing $.37 and the rest costing $.22 she paid the postal clerk a total of $13.25 for all the stamps how many of each type of stamps Did liv buy

Answer 1

Let \( x \) be the number of stamps that cost $0.37, and let \( y \) be the number of stamps that cost $0.22. We can set up the following system of equations based on the information provided:

1. The total number of stamps is 50:
\[
x + y = 50
\]

2. The total cost of the stamps is $13.25:
\[
0.37x + 0.22y = 13.25
\]

Now, we can solve this system of equations. First, we can solve the first equation for \( y \):
\[
y = 50 - x
\]

Next, we can substitute \( y \) in the second equation:
\[
0.37x + 0.22(50 - x) = 13.25
\]

Expanding the equation:
\[
0.37x + 11 - 0.22x = 13.25
\]

Combining like terms:
\[
(0.37 - 0.22)x + 11 = 13.25
\]
\[
0.15x + 11 = 13.25
\]

Now, isolate \( x \):
\[
0.15x = 13.25 - 11
\]
\[
0.15x = 2.25
\]
\[
x = \frac{2.25}{0.15} = 15
\]

Now that we have \( x \), we can find \( y \):
\[
y = 50 - x = 50 - 15 = 35
\]

So, Liv bought:
- \( 15 \) stamps costing $0.37
- \( 35 \) stamps costing $0.22

To verify, we can check the total cost:
\[
15(0.37) + 35(0.22) = 5.55 + 7.70 = 13.25
\]

Thus, the calculations confirm that the results are correct. Liv bought **15 stamps** at $0.37 and **35 stamps** at $0.22.