X = 30 1/4 - 20 + 3 1/5

Y = 1% x 2250

2X < 3Y

Let's break down and solve the system step by step:

### 1. Solving for \( X \):

Given:
\[
X = 30 \frac{1}{4} - 20 + 3 \frac{1}{5}
\]

First, convert the mixed numbers into improper fractions:

- \( 30 \frac{1}{4} = \frac{121}{4} \)
- \( 3 \frac{1}{5} = \frac{16}{5} \)

Now, combine everything:
\[
X = \frac{121}{4} - 20 + \frac{16}{5}
\]

To add these terms, first convert everything to a common denominator. The least common denominator of 4 and 5 is 20.

\[
\frac{121}{4} = \frac{605}{20}, \quad 20 = \frac{400}{20}, \quad \frac{16}{5} = \frac{64}{20}
\]

Now, substitute these values into the expression:
\[
X = \frac{605}{20} - \frac{400}{20} + \frac{64}{20}
\]
\[
X = \frac{605 - 400 + 64}{20} = \frac{269}{20}
\]
Thus, \( X = \frac{269}{20} \approx 13.45 \).

### 2. Solving for \( Y \):

Given:
\[
Y = 1\% \times 2250
\]
\[
Y = \frac{1}{100} \times 2250 = 22.50
\]

### 3. Solving the inequality \( 2X < 3Y \):

Substitute the values of \( X \) and \( Y \) into the inequality:

\[
2X = 2 \times \frac{269}{20} = \frac{538}{20} = 26.90
\]
\[
3Y = 3 \times 22.50 = 67.50
\]

Now, check if the inequality holds:
\[
26.90 < 67.50
\]

The inequality \( 2X < 3Y \) is **true**.

---

Would you like more details on any step? 

Here are some related questions to explore:
1. How do you convert mixed numbers to improper fractions?
2. What is the process to solve inequalities involving fractions?
3. How can percentages be calculated efficiently?
4. What is the least common denominator and how is it found?
5. Can you explain the concept of inequalities further?

**Tip**: When adding or subtracting fractions, always remember to find the least common denominator for accurate results!

Learn how to solve the inequality 2X < 3Y, involving mixed numbers, percentages, and basic algebra. This problem includes step-by-step instructions on converting mixed numbers to improper fractions, calculating percentages, and manipulating inequalities. Suitable for Grades 6-8 students.

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