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Let's break down and solve this problem step by step.

### Part (a): How many macaroons did Mrs. Yang bake?

Let the total number of macaroons Mrs. Yang baked be $ x $.

- $ \frac{3}{4} $ of the macaroons were chocolate.
- The rest were strawberry, meaning $ \frac{1}{4} $ were strawberry.

So, she sold:
- $ \frac{5}{6} $ of the chocolate macaroons.
- $ \frac{3}{8} $ of the strawberry macaroons.

The macaroons left are:
- $ 1 - \frac{5}{6} = \frac{1}{6} $ of the chocolate macaroons were left.
- $ 1 - \frac{3}{8} = \frac{5}{8} $ of the strawberry macaroons were left.

According to the problem, after selling, Mrs. Yang had 81 macaroons left in total.

The number of chocolate macaroons left:
\[
\frac{1}{6} \times \frac{3}{4}x = \frac{x}{8}
\]

The number of strawberry macaroons left:
\[
\frac{5}{8} \times \frac{1}{4}x = \frac{5x}{32}
\]

The total macaroons left is the sum of these two:
\[
\frac{x}{8} + \frac{5x}{32} = 81
\]

To solve this equation, first get a common denominator:
\[
\frac{4x}{32} + \frac{5x}{32} = 81
\]
\[
\frac{9x}{32} = 81
\]
Multiply both sides by 32:
\[
9x = 2592
\]
Divide by 9:
\[
x = 288
\]

So, Mrs. Yang baked **288 macaroons**.

### Part (b): How much did she collect from the sale of the macaroons?

She sold the macaroons at 3 for $7. Let's first calculate how many macaroons she sold.

- She sold $ \frac{5}{6} $ of the chocolate macaroons, which is:
  \[
  \frac{5}{6} \times \frac{3}{4} \times 288 = 180 \text{ chocolate macaroons.}
  \]

- She sold $ \frac{3}{8} $ of the strawberry macaroons, which is:
  \[
  \frac{3}{8} \times \frac{1}{4} \times 288 = 27 \text{ strawberry macaroons.}
  \]

The total macaroons sold:
\[
180 + 27 = 207
\]

Now, each 3 macaroons are sold for $7, so the total amount collected is:
\[
\frac{207}{3} \times 7 = 69 \times 7 = 483
\]

Therefore, Mrs. Yang collected **$483** from the sale of the macaroons.

---

Would you like more details on any of the steps or have further questions?

Here are five related questions to practice:
1. What would happen if Mrs. Yang sold $ \frac{4}{6} $ of the chocolate macaroons instead?
2. How many macaroons would be left if Mrs. Yang had baked 350 macaroons instead of 288?
3. If the price per set of 3 macaroons was raised to $9, how much would Mrs. Yang collect?
4. How many strawberry macaroons did Mrs. Yang start with?
5. If Mrs. Yang had sold all the chocolate macaroons, how many would she have left?

**Tip:** When dealing with fractions in word problems, it's helpful to write down each fraction and understand how they relate to the total quantity.

Mrs. Yang baked some macaroons. 3/4 of them were chocolate macaroons and the rest were strawberry macaroons. She sold 5/6 of the chocolate macaroons and 3/8 of the strawberry macaroons. After that, she had 81 macaroons left.
(a) How many macaroons did Mrs. Yang bake?
(b) She sold the macaroons at 3 for $7. How much did she collect from the sale of the macaroons?

Learn how to calculate the total number of macaroons Mrs. Yang baked and how much she collected from sales using fractions and algebra. Step-by-step solution provided. Suitable for Grades 5-7.

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