Divide 1400 into three parts such that the 1st part is 2/3 of the 2nd part and the ratio between the 2nd and 3rd part is 4:5. Find each part.

Let’s denote the three parts as A, B, and C.

According to the problem:

• The total sum of the parts is A + B + C = 1400.
• The first part, A, is 2/3 of the second part, B. This gives us the equation: A = (2/3)B.
• The ratio between the second part and the third part is B/C = 4/5, which means B = (4/5)C.

Now, we can express both A and C in terms of B.

From A = (2/3)B, we have:

• A = (2/3)B

From B = (4/5)C, rewriting it gives:

• C = (5/4)B

Now, substituting these into the total sum equation:

A + B + C = 1400

becomes:

(2/3)B + B + (5/4)B = 1400

To add the fractions, we need a common denominator. The common denominator for 3 and 4 is 12.

So, rewriting these fractions:

• (2/3)B = (8/12)B
• B = (12/12)B
• (5/4)B = (15/12)B

Now, our equation looks like this:

(8/12)B + (12/12)B + (15/12)B = 1400

This simplifies to:

(35/12)B = 1400

To isolate B, multiply both sides by the reciprocal of (35/12):

B = 1400 * (12/35)

This calculation gives us:

B = 480

Now that we have B, we can find A and C:

• A = (2/3)B = (2/3)*480 = 320
• C = (5/4)B = (5/4)*480 = 600

So, the three parts are:

• A = 320
• B = 480
• C = 600

To summarize, the three parts of 1400 are:

• First Part (A): 320
• Second Part (B): 480
• Third Part (C): 600