Let's determine how many [tex]$1 stamps and $[/tex]1.20 stamps Angela bought given that she bought a total of 10 stamps that cost her [tex]$11 altogether.
We can set up two equations to solve this problem:
1. The total number of stamps equation:
\[ x + y = 10 \]
where \( x \) represents the number of $[/tex]1 stamps and [tex]\( y \)[/tex] represents the number of [tex]$1.20 stamps.
2. The total cost equation:
\[ 1x + 1.20y = 11 \]
First, let's solve the first equation for \( y \):
\[ y = 10 - x \]
Next, we substitute \( y \) in the second equation:
\[ 1x + 1.20(10 - x) = 11 \]
Now, distribute and combine like terms:
\[ x + 12 - 1.20x = 11 \]
Combine \( x \) terms:
\[ -0.20x + 12 = 11 \]
Subtract 12 from both sides:
\[ -0.20x = -1 \]
Next, divide both sides by -0.20:
\[ x = \frac{-1}{-0.20} = 5 \]
So, Angela bought 5 stamps that cost $[/tex]1 each.
To find [tex]\( y \)[/tex], substitute [tex]\( x = 5 \)[/tex] back into the equation [tex]\( y = 10 - x \)[/tex]:
[tex]\[ y = 10 - 5 = 5 \][/tex]
So, Angela also bought 5 stamps that cost [tex]$1.20 each.
In conclusion, Angela bought:
- 5 stamps that cost $[/tex]1 each
- 5 stamps that cost $1.20 each
