Cindy bought 81 plums and mangoes altogether> she gave 20% of the plums and 25% of the mangoes to Betty. If Betty got 18 fruits, how many plums did Cindy buy?


Let's denote the number of plums Cindy bought as \( p \) and the number of mangoes as \( m \).

According to the problem:
\[
p + m = 81
\]
Cindy gave 20% of the plums and 25% of the mangoes to Betty, and Betty received a total of 18 fruits. Therefore, we can write:
\[
0.2p + 0.25m = 18
\]

Now, we have a system of two equations:
1. \( p + m = 81 \)
2. \( 0.2p + 0.25m = 18 \)

Let's solve this system step by step.

### Step 1: Simplify the second equation.
Multiply the second equation by 100 to eliminate the decimals:
\[
20p + 25m = 1800
\]

### Step 2: Simplify further by dividing by 5:
\[
4p + 5m = 360
\]

### Step 3: Solve the system of equations.
Now, we have:
1. \( p + m = 81 \)
2. \( 4p + 5m = 360 \)

Let's solve for \( p \) and \( m \) using substitution or elimination. We'll use substitution here.

From the first equation:
\[
m = 81 - p
\]

Substitute \( m = 81 - p \) into the second equation:
\[
4p + 5(81 - p) = 360
\]
\[
4p + 405 - 5p = 360
\]
\[
-p + 405 = 360
\]
\[
-p = 360 - 405
\]
\[
-p = -45
\]
\[
p = 45
\]

So, Cindy bought **45 plums**.

Would you like a detailed explanation or do you have any questions?

Here are 5 related questions:
1. How many mangoes did Cindy buy?
2. How many fruits did Betty receive that were mangoes?
3. If Cindy had given 30% of the plums to Betty instead, how many plums would Betty have received?
4. What would be the new total number of fruits Cindy had if she bought 10 more mangoes?
5. What percentage of the total fruits did Betty receive?

**Tip:** When solving systems of equations, substitution and elimination are effective methods to find unknown variables.

Learn how to solve the problem where Cindy bought 81 plums and mangoes altogether, and gave 20% of the plums and 25% of the mangoes to Betty, who received 18 fruits in total. Discover the step-by-step solution using systems of equations and percentages. Suitable for Grades 7-9.

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