Answer:
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
