A rope measuring 816 cm long was cut into 3 pieces and Z .
X was thrice as long as was 80 cm shorter than X . What was the length
of Y ?

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Mar 26,2025

Question

A rope measuring 816 cm long was cut into 3 pieces $$ \mathrm{X}, \mathrm{Y} $$ and Z . X was thrice as long as $$ \mathrm{Y} . \mathrm{Z} $$ was 80 cm shorter than X . What was the length of Y ?

UpStudy AI · Accepted Answer

Let $$ Y $$ be the length of piece Y. Then according to the problem:

1. $$ X = 3Y $$ (X is thrice as long as Y).
2. $$ Z = X - 80 $$ (Z is 80 cm shorter than X).

The sum of the three pieces is the total length of the rope, so:

$$
Y + X + Z = 816
$$

Substitute the expressions of $$ X $$ and $$ Z $$:

$$
Y + 3Y + (3Y - 80) = 816
$$

Combine like terms:

$$
7Y - 80 = 816
$$

Add 80 to both sides:

$$
7Y = 896
$$

Divide by 7:

$$
Y = \frac{896}{7} = 128
$$

Thus, the length of piece $$ Y $$ is $$ 128 $$ cm.
The length of Y is 128 cm.

A rope measuring 816 cm long was cut into 3 pieces and Z .
X was thrice as long as was 80 cm shorter than X . What was the length
of Y ?

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A rope measuring 816 cm long was cut into 3 pieces and Z . X was thrice as long as was 80 cm shorter than X . What was the length of Y ?