Question

Lisa is stringing beads to make a necklace, anklet, and a bracelet. The necklace uses 50% of the string. The anklet is 60% shorter than the necklace. The bracelet needs 25% less string than the anklet. How long is the original, uncut string if the bracelet measures 18 cm

Answer 1

Answer:

The Original length of uncut String is of 120 cm.

Step-by-step explanation:

Let the length of original string be x.

Length of bracelet = 18 cm.

The necklace uses 50% of the string

Hence length of necklace will be equal to 50% of the string.

Length of necklace = $\frac{50}{100}\timesx =0.5x$

The anklet is 60% shorter than the necklace.

Length of anklet will be equal to difference of Length of necklace and 60%  of the Length of necklace.

Length of anklet = $0.5x-\frac{60}{100}\times0.5x = 0.5x-0.3x = 0.2x$

The bracelet needs 25% less string than the anklet.

Length of bracelet will be equal to difference of Length of anklet and 25%  of the Length of anklet.

Length of bracelet = $0.2x-\frac{25}{100}\times0.2x = 0.2x-0.05x = 0.15x$

But Length of Bracelet = 18 cm

$\therefore 0.15x=18\ cm\\\\x = \frac{18}{0.15}\ cm = 120\ cm$

Hence Total original Length of Uncut String is 120 cm.