If the ratio of the lengths of two ropes is 5:7 and the total length of the rope

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Question: If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?

Options:

Correct Answer: 25

Solution:

Let the lengths be 5x and 7x. Given 5x + 7x = 72, 12x = 72, x = 6. Therefore, shorter rope = 5x = 5*6 = 30.

If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?

If the ratio of the lengths of two ropes is 5:7 and the total length of the ropes is 72 meters, what is the length of the shorter rope?

Step 1: Understand that the lengths of the two ropes are in a ratio of 5:7. This means for every 5 parts of the shorter rope, there are 7 parts of the longer rope.
Step 2: Let 'x' be a common multiplier. Then, the length of the shorter rope can be represented as 5x and the length of the longer rope as 7x.
Step 3: Write an equation for the total length of the ropes. Since the total length is 72 meters, we can write: 5x + 7x = 72.
Step 4: Combine the terms on the left side of the equation. This gives us: 12x = 72.
Step 5: Solve for 'x' by dividing both sides of the equation by 12. This gives us: x = 72 / 12, which simplifies to x = 6.
Step 6: Now, find the length of the shorter rope by substituting 'x' back into the expression for the shorter rope: 5x = 5 * 6.
Step 7: Calculate 5 * 6, which equals 30. Therefore, the length of the shorter rope is 30 meters.

Ratios – Understanding and applying the concept of ratios to determine proportional lengths.
Algebraic Equations – Setting up and solving linear equations based on given relationships.
Word Problems – Translating a real-world scenario into a mathematical equation.