Please help in solving this math

Question

Lily cuts a piece of yarn into three pieces. The second pieces is 3 times as long as the first piece, and the third piece is 6 centimeters longer than the first piece. If the total length of the yarn is 211 centimeters, find the lengths of each of the three pieces.

Answer 1

X + 3x + x+6 = 211

5x + 6 = 211

5x = 205

x = 41

41, 123, 47

Answer 2

In this case we have 3 unknowns, therefore we must have 3 equations to solve it.

Let x = length of the first piece

y = length of the second piece

z = length of the third piece

Eq. I: y = 3x

Eq. II: z = x + 6

Eq. III: x + y + z = 211

By using the values of y and z in terms of x from the first 2 equations, we can solve for x:

y = 3x Eq. I

z = x + 6 Eq. II

x + y + z = 211 Eq. III

x + (3x) + (x + 6) = 211 substituting for y and z in terms of x

5x + 6 = 211 simplify

5x = 211 - 6 subtract 6 from both sides to isolate the x term

5x = 205 simplify

x = 205/5 divide both sides to isolate x

x = 41 solve for x

Using this value for x in both Eq. I & II we can solve for y and z directly:

y = 3x Eq. I

y = 3(41) substitute 41 for x

y = 123 solve for y

z = x + 6 Eq. II

z = 41 + 6 substitute 41 for x

z = 47 solve for z

Therefore, piece 1 is 41cm long, piece 2 is 123cm long and piece 3 is 47cm long.

Hope this helps!