Question

Nancy has 3 necklaces of different lengths. When placed in a stretched out line, they are 445
mm long. Necklace A is 45 mm longer than Necklace B, and Necklace B is half as long as
Necklace C. How long is Necklace A?

Answer 1

The given relationships is that Necklace B is the shortest of the 3

necklaces and Necklace C would be the longest.

• Necklace A is 145 mm long

Reasons:

The number of necklaces = 3

Sum of the lengths of the necklaces = 445 mm

Length of Necklace A = 45 mm + Length of Necklace B

$\displaystyle Length \ of \ Necklace \ B = \mathbf{\frac{Length \ of \ Necklace \ C}{2}}$

Required:

The length of Necklace A

Solution:

Let A represent Necklace A, B represent Necklace B, and C represent

Necklace C, we have;

A + B + C = 445

A = B + 45

$\displaystyle B = \frac{C}{2}$

Therefore;

B = A - 45

2×B = C

2 × (A - 45) = C

Which gives;

A + A - 45 + 2 × (A - 45) = 445

4·A - 135 = 445

$\displaystyle A = \frac{445 + 135}{4} = \mathbf{145}$

The length of Necklace A = 145 mm

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