A rope was cut into two pieces in the ratio 7:9 if one was longer by 6cm,what are the lengths of the two pieces?

a.21 cm and 27 cm
b.24 cm and 30 cm
c.26 cm and 32 cm
d.31 cm and 37 cm

Please help me how to answer this..its for my report thank you

27/21 = 9/7 * 3/3

the others do not work

x/(x+6) = 7/9

9x = 7(x+6)
9x = 7x + 42
2x = 42
x = 21
so, x+6 = 27

Well, it seems like we have a little string problem here. Let me help you unravel it.

Let's call the length of the first piece 7x, and the length of the second piece 9x. According to the problem, the second piece is longer by 6 cm. So, we have the equation 9x - 7x = 6.

Simplifying, we get 2x = 6. Dividing both sides by 2, we find that x = 3.

So, the length of the first piece is 7x = 7 * 3 = 21 cm, and the length of the second piece is 9x = 9 * 3 = 27 cm.

Therefore, option a, 21 cm and 27 cm, is the correct answer.

To solve this problem, we can set up the equation based on the given information.

Let's assume the lengths of the two pieces of the rope are 7x cm and 9x cm, where x is a common factor.

According to the problem, one piece is longer by 6 cm. So we can write another equation:

9x - 7x = 6

Simplifying the equation, we have:

2x = 6

Dividing both sides by 2, we find:

x = 3

Now, we can substitute the value of x back into the lengths of the two pieces:

First piece: 7x = 7 * 3 = 21 cm
Second piece: 9x = 9 * 3 = 27 cm

Therefore, the lengths of the two pieces are 21 cm and 27 cm.

Hence, the correct option is a. 21 cm and 27 cm.

To solve this problem, we can use a proportion.

Let's assume that the length of the original rope is represented by 'x' cm.
According to the problem, the rope was cut into two pieces in the ratio 7:9. This means the lengths of the two pieces will be (7x/16) cm and (9x/16) cm, respectively.

We are also given that one piece is longer by 6 cm. Based on this information, we can set up the equation:

(7x/16) + 6 = (9x/16)

To solve for 'x', we can multiply both sides of the equation by 16 to eliminate the denominators:

7x + 96 = 9x

Rearranging the terms, we have:

9x - 7x = 96

2x = 96

Dividing both sides by 2, we get:

x = 48

Now we can substitute the value of 'x' back into the expression for the lengths of the two pieces:

7x/16 = 7*48/16 = 21 cm

9x/16 = 9*48/16 = 27 cm

Therefore, the lengths of the two pieces are 21 cm and 27 cm, respectively.

So, the correct answer is option (a) 21 cm and 27 cm.