If $\frac{2}{3}$ part of any number is 4 greater than$\frac{3}{5}$ part of this number. Find this number

Q: If $\frac{2}{3}$ part of any number is 4 greater than$\frac{3}{5}$ part of this number. Find this number

To solve the problem, we need to find a number $ x $ such that $\frac{2}{3}$ of this number is 4 greater than $\frac{3}{5}$ of the same number. Let's set up the equation based on this information: \[ \frac{2}{3}x = \frac{3}{5}x + 4 \] To eliminate the fractions, we can multiply every term by 15, which is the least common multiple of 3 and 5: \[ 15 \times \frac{2}{3}x = 15 \times \frac{3}{5}x + 15 \times 4 \] This simplifies to: \[ 10x = 9x + 60 \] Subtract $ 9x $ from both sides: \[ 10x - 9x = 60 \] \[ x = 60 \] Thus, the number we are looking for is 60, which corresponds to Option 3. **Explanation for why Option 3 is correct:** The equation derived from the problem statement leads us directly to the solution $ x = 60 $. By substituting back into the original condition, we can verify: - $\frac{2}{3} \times 60 = 40$ - $\frac{3}{5} \times 60 = 36$ Indeed, 40 is 4 greater than 36, confirming that our solution satisfies the condition given in the problem. **Explanation for why the other options are incorrect:** 1. **Option 1: 30** - $\frac{2}{3} \times 30 = 20$ - $\frac{3}{5} \times 30 = 18$ - The difference is 2, not 4, so this does not satisfy the condition. 2. **Option 2: 40** - $\frac{2}{3} \times 40 = 26.67$ - $\frac{3}{5} \times 40 = 24$ - The difference is 2.67, not 4, so this does not satisfy the condition. 3. **Option 4: 20** - $\frac{2}{3} \times 20 = 13.33$ - $\frac{3}{5} \times 20 = 12$ - The difference is 1.33, not 4, so this does not satisfy the condition. Therefore, Option 3 is the only correct answer, as it is the only option that satisfies the condition given in the problem.

Question

Accepted Answer

To solve the problem, we need to find a number $ x $ such that $\frac{2}{3}$ of this number is 4 greater than $\frac{3}{5}$ of the same number. Let's set up the equation based on this information:

$$
\frac{2}{3}x = \frac{3}{5}x + 4
$$

To eliminate the fractions, we can multiply every term by 15, which is the least common multiple of 3 and 5:

$$
15 \times \frac{2}{3}x = 15 \times \frac{3}{5}x + 15 \times 4
$$

This simplifies to:

$$
10x = 9x + 60
$$

Subtract $ 9x $ from both sides:

$$
10x - 9x = 60
$$

$$
x = 60
$$

Thus, the number we are looking for is 60, which corresponds to Option 3.

**Explanation for why Option 3 is correct:**

The equation derived from the problem statement leads us directly to the solution $ x = 60 $. By substituting back into the original condition, we can verify:

- $\frac{2}{3} \times 60 = 40$
- $\frac{3}{5} \times 60 = 36$

Indeed, 40 is 4 greater than 36, confirming that our solution satisfies the condition given in the problem.

**Explanation for why the other options are incorrect:**

1. **Option 1: 30**
   - $\frac{2}{3} \times 30 = 20$
   - $\frac{3}{5} \times 30 = 18$
   - The difference is 2, not 4, so this does not satisfy the condition.

2. **Option 2: 40**
   - $\frac{2}{3} \times 40 = 26.67$
   - $\frac{3}{5} \times 40 = 24$
   - The difference is 2.67, not 4, so this does not satisfy the condition.

3. **Option 4: 20**
   - $\frac{2}{3} \times 20 = 13.33$
   - $\frac{3}{5} \times 20 = 12$
   - The difference is 1.33, not 4, so this does not satisfy the condition.

Therefore, Option 3 is the only correct answer, as it is the only option that satisfies the condition given in the problem.