Question

There are three ropes of different length. The third rope is 9m longer than the second rope. The second rope is 7m longer than the first rope. If the length of the three ropes is 98m, how long is each rope?

Answer 1

Answer :-

• Length of the first rope = 25 m.

• Length of the second rope = 32 m.

• Length of the third rope = 41 m.

Given :-

• There are three ropes of different length.

• The third rope is 9 m longer than the second rope.

• The second rope is 7 m longer than the first rope.

• The length of the three ropes is 98 m.

To find :-

• The length of each rope.

Step-by-step explanation :-

• Let the length of the first rope be x.

• Then the length of the second rope will be x + 7, since it's 7 m longer than the first rope.

• Now, at last the length of the third rope will be x + 7 + 9, because it's 9 m longer than the second rope and the second rope is x + 7.

• Now, the length of the three ropes is 98 cm, that means the sum of the length of the three ropes must be equal to 98 m.

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$\rightarrow \sf x + (x + 7) + (x + 7 + 9) = 98$

Removing the brackets,

$\rightarrow \sf x + x + 7 + x + 7 + 9 = 98$

Keeping the constants and variables separately in brackets,

$\rightarrow\sf(x + x + x) + (7 + 7 + 9) = 98$

On simplifying,

$\sf \rightarrow(3x) + (14 + 9) = 98$

Removing the brackets,

$\sf\rightarrow3x + 23 = 98$

Transposing 23 from LHS to RHS, changing it's sign,

$\sf \rightarrow3x = 98 - 23$

Subtracting 23 from 98,

$\rightarrow\sf3x = 75$

Transposing 3 from LHS to RHS, changing it's sign,

$\rightarrow\sf x = \dfrac{75}{3}$

Dividing 75 by 3,

$\overline{\boxed{\rightarrow\sf x = 25 \: m}}$

• The value of x is 25 m.

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Hence, the length of all the ropes are as follows :-

$\bf x = 25 \: m.$

$\bf x + 7 = 25 + 7 = 32 \: m.$

$\bf x + 7 + 9 = 25 + 7 + 9 = 41 \: m.$