Question

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
𝑐
) and cakes (k
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

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**.