To solve this problem, let's break it down step-by-step.
a) We need to create an equation that represents the total amount of money raised from selling cookies and cakes.
Let:
- \( c \) = number of cookies sold
- \( k \) = number of cakes sold
The money earned from cookies is \( 2c \) (since each cookie is sold for $2) and from cakes is \( 10k \) (since each cake is sold for $10). According to the problem, the total amount raised is $800.
Therefore, the equation can be written as:
\[ 2c + 10k = 800 \]
b) Now, if the community center sold a total of 36 cakes, we can substitute \( k = 36 \) into the previously derived equation.
So we substitute \( k \) into the equation:
\[ 2c + 10(36) = 800 \]
Calculating \( 10(36) \):
\[ 2c + 360 = 800 \]
Next, subtract 360 from both sides:
\[ 2c = 800 - 360 \] \[ 2c = 440 \]
Now, divide both sides by 2 to find \( c \):
\[ c = \frac{440}{2} \] \[ c = 220 \]
Thus, the community center sold 220 cookies.