5th grade math question

Question

A blue rope is three times as long as a red rope. A green rope is 5 times as long as the blue rope. If the total length of the three ropes is 508.25 meters, what is the length of the blue rope?

Answer 1

 

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

 

The length of the blue rope is 80.25 meters.