lorna had one third the number of coins that mandy collected. mandy collected two and one quarter the number of coins collected by enver. if all three collected 480 coins then how many coins did mandy collect?

Let the number of coins collected by Enver be denoted by \( x \).

1. Mandy collected \( \frac{9}{4} \) times the number of coins Enver collected, so the number of coins Mandy collected is \( \frac{9}{4}x \).
2. Lorna collected one third the number of coins Mandy collected, so the number of coins Lorna collected is \( \frac{1}{3} \times \frac{9}{4}x = \frac{3}{4}x \).

Given that the total number of coins collected by all three is 480, we can write the equation:
\[
x + \frac{9}{4}x + \frac{3}{4}x = 480
\]

To solve for \( x \), first combine the terms on the left-hand side:
\[
x + \frac{9}{4}x + \frac{3}{4}x = \left(1 + \frac{9}{4} + \frac{3}{4}\right)x = \left(\frac{4}{4} + \frac{9}{4} + \frac{3}{4}\right)x = \frac{16}{4}x = 4x
\]

So, the equation simplifies to:
\[
4x = 480
\]

Dividing both sides by 4 gives:
\[
x = 120
\]

Now that we know Enver collected 120 coins, we can calculate the number of coins Mandy collected:
\[
\text{Mandy's coins} = \frac{9}{4} \times 120 = \frac{9 \times 120}{4} = \frac{1080}{4} = 270
\]

Thus, Mandy collected **270 coins**.

Would you like more details, or do you have any questions?

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Here are some related questions you might find interesting:

1. How many coins did Lorna collect?
2. What is the ratio of the coins collected by Mandy to Enver?
3. If Mandy had collected twice as many coins as she did, what would the new total be?
4. How would the total change if Enver collected 50 more coins?
5. What fraction of the total coins did Lorna collect?
6. What is the percentage of coins collected by Mandy out of the total?
7. If the total number of coins was 600, how many coins would Mandy collect?
8. How many coins would each have if the total was divided equally?

**Tip:** Always double-check your units and ensure they are consistent throughout the problem.

Explore how to calculate the number of coins collected by Mandy in a coin collection problem involving proportions and algebraic equations. Learn step-by-step how to solve for Mandy's coins in relation to Enver and Lorna. Suitable for Grades 7-9.

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