There was a total of 640 pears and apples at Mr Li's stall. The ratio of the numbers of pears to the  number of apples was 9:7. After he sold an equal number of each type of fruits, the number of pears and apples left was in the ratio 9:4. How many pears and apples did he sell altogether?




Let's denote the initial number of pears by \( p \) and the initial number of apples by \( a \).

Given that the total number of pears and apples is 640, and the initial ratio of pears to apples is 9:7, we can set up the following equations:

\[
p + a = 640
\]
\[
\frac{p}{a} = \frac{9}{7}
\]

From the ratio equation, express \( p \) in terms of \( a \):

\[
p = \frac{9}{7}a
\]

Substituting \( p = \frac{9}{7}a \) into the total equation:

\[
\frac{9}{7}a + a = 640
\]

Multiplying through by 7 to eliminate the fraction:

\[
9a + 7a = 640 \times 7
\]
\[
16a = 4480
\]
\[
a = 280
\]

Thus, the initial number of apples is \( a = 280 \). Substituting this back to find \( p \):

\[
p = \frac{9}{7} \times 280 = 360
\]

So, initially, there were 360 pears and 280 apples.

### Step 2: Setting up the final condition

After selling an equal number of pears and apples, the remaining fruits had a ratio of 9:4. Let the number of fruits sold be \( x \). Therefore:

- The remaining number of pears is \( 360 - x \).
- The remaining number of apples is \( 280 - x \).

We are given that the ratio of the remaining pears to apples is 9:4:

\[
\frac{360 - x}{280 - x} = \frac{9}{4}
\]

Cross-multiply to solve for \( x \):

\[
4(360 - x) = 9(280 - x)
\]
\[
1440 - 4x = 2520 - 9x
\]
\[
5x = 1080
\]
\[
x = 216
\]

Thus, Mr. Li sold **216 pears** and **216 apples**. The total number of fruits sold altogether is:

\[
216 + 216 = 432
\]

### Final Answer:
Mr. Li sold **432 fruits** altogether.

Would you like a more detailed breakdown or have any questions about the solution? Here are some related problems:

1. What if the total number of fruits was 800, but the same ratios applied?
2. How many fruits would he sell if the final ratio was 5:3 instead of 9:4?
3. If he sold 250 fruits in total, what would the new final ratio of pears to apples be?
4. What is the percentage of apples sold from the total apples?
5. If the price per pear is twice that of an apple, what is the total revenue from selling 432 fruits?

**Tip:** When solving ratio problems, converting the ratio into fractions can make it easier to set up equations and find solutions.

There was a total of 640 pears and apples at Mr Li's stall. The ratio of the numbers of pears to the number of apples was 9:7. After he sold an equal number of each type of fruits, the number of pears and apples left was in the ratio 9:4. How many pears and apples did he sell altogether?

Learn how to solve a problem involving the ratio of pears to apples and finding out how many fruits were sold at Mr. Li's stall. This solution covers key mathematical concepts such as ratios, algebraic equations, and cross-multiplication. Suitable for students in Grades 6-8.

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