A baked some cookies. 60% of the cookies are butter cookies and the rest are chocolate chip cookies. She then gave a third of the butter cookies to her friends and had 22 butter cookies left. How many cookies did she bake altogether?


Let the total number of cookies A baked be \( x \). According to the problem, 60% of the cookies are butter cookies, so the number of butter cookies is:

\[
0.6x
\]

A gave away a third of the butter cookies to her friends, meaning she kept two-thirds of them. After giving some away, A had 22 butter cookies left. This can be written as:

\[
\frac{2}{3} \times 0.6x = 22
\]

Now, solve for \( x \):

\[
0.4x = 22
\]

\[
x = \frac{22}{0.4} = 55
\]

Therefore, A baked a total of **55 cookies**.

Would you like further explanation or details on how the steps were derived?

Here are 5 related questions to explore:
1. If A had 25 butter cookies left instead, how many cookies would she have baked?
2. What percentage of the cookies were chocolate chip cookies?
3. If A had baked 10 more cookies, how many more butter cookies would there be?
4. How many chocolate chip cookies did A bake?
5. If A had given half of the butter cookies to her friends, how many butter cookies would she have left?

**Tip:** When solving word problems, carefully translate the problem into an equation step-by-step, assigning variables where needed!

A baked some cookies. 60% of the cookies are butter cookies and the rest are chocolate chip cookies. She then gave a third of the butter cookies to her friends and had 22 butter cookies left. How many cookies did she bake altogether?

Discover how to solve a word problem where 60% of the cookies are butter cookies, and A gave a third of them away, leaving her with 22 butter cookies. This detailed explanation involves using percentages and linear equations, suitable for students in Grades 6-8.

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