Answer:

1152

Step-by-step explanation:

Let's break down the problem step by step. Let the number be represented as "x."

3/5th of 2/3rd of the number is (3/5) * (2/3) * x, which simplifies to (2/5) * x.

3/5th of 1/4th of the same number is (3/5) * (1/4) * x, which simplifies to (3/20) * x.

Now, you're given that the difference between these two expressions is 288:

(2/5) * x - (3/20) * x = 288

To solve for x, you can combine the fractions:

(8/20) * x - (3/20) * x = 288

Now, you can subtract the second expression from the first:

(8/20 - 3/20) * x = 288

(5/20) * x = 288

Simplify the fraction on the left side:

(1/4) * x = 288

Now, isolate x by multiplying both sides by 4:

x = 288 * 4

x = 1152

So, the number is 1152.

Answer:

Let's break down the problem step by step.

Let "x" be the number you want to find.

1. "3/5 of 2/3 of a number" can be expressed as (3/5) * (2/3) * x = (6/15) * x = (2/5) * x.

2. "3/5 of 1/4 of the same number" can be expressed as (3/5) * (1/4) * x = (3/20) * x.

Now, you are given that the difference between these two expressions is 288:

(2/5) * x - (3/20) * x = 288

To solve for "x," you can first find a common denominator for the fractions:

(8/20) * x - (3/20) * x = 288

Now, combine the fractions:

(8/20 - 3/20) * x = 288

(5/20) * x = 288

Simplify further:

(1/4) * x = 288

Now, isolate "x" by multiplying both sides by 4:

x = 288 * 4

x = 1152

So, the number you are looking for is 1152.