A blue rope is three times as long as the red rope. A green rope is five times as long as the blue rope. If the total length is 508.25 meters, what is the length of the blue rope?

The length of the blue rope is 80.25 meters.

Step-by-step explanation:

B = Blue Rope

G = Green Rope

R = Red Rope

B=3R (Blue is 3 x as long as Red)

G=5B (Green is 5 x as long as Blue)

B+G+R = 508.25 (The three ropes together are 508.25 meters)

Since B=3R, I will rewrite the equation above

3R + G + R = 508.25

Now, I will write G in terms of R:

G=5B

B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.

Rewrite the equation again in terms of R:

3R + 15R + R = 508.25

19R = 508.25 (combine like terms)

R = 26.75 (divide both sides by 19 to solve for R)

Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):

B=3R

B=3 (26.75)

B=80.25 meters