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