To support a local charity, a community center hosted a bake sale. Cookies were sold for $2 each, and cakes were sold for $10 each. A total of $800 was raised from the bake sale. a) Which equation can be used to represent how many cookies (c ) and cakes (k ) were sold? b) If the community center sold a total of 36 cakes, how many cookies did they sell? cookies were sold.

Answer 1

Let's break it down step by step.

a) To represent how many cookies (c) and cakes (k) were sold, we can create an equation based on the total revenue raised from both the cookies and cakes. The sales prices are $2 for cookies and $10 for cakes. The total amount raised is $800. Therefore, the equation representing this situation is:

\[ 2c + 10k = 800 \]

b) If the community center sold a total of 36 cakes, we can substitute \( k = 36 \) into the equation to find out how many cookies were sold.

Substituting \( k \) into the equation:

\[ 2c + 10(36) = 800 \] \[ 2c + 360 = 800 \]

Now, subtract 360 from both sides:

\[ 2c = 800 - 360 \] \[ 2c = 440 \]

Now, divide both sides by 2 to solve for \( c \):

\[ c = \frac{440}{2} \] \[ c = 220 \]

Thus, the community center sold 220 cookies.