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

The Original length of uncut String is of 120 cm.

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 =
`(50)/(100)*x =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-(60)/(100)*0.5x = 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-(25)/(100)*0.2x = 0.2x-0.05x = 0.15x`

But Length of Bracelet = 18 cm

`\therefore 0.15x=18\ cm\\\\x = (18)/(0.15)\ cm = 120\ cm`

Hence Total original Length of Uncut String is 120 cm.