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sergeinik [125]
3 years ago
8

The price of diamond varies directly as square of its weight. The price of a 12 decigrams diamond is $7200. If diamond breaks in

to two pieces whose weights are in the ratio 3:1, find the loss incurred.
Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0
--------------------------------------------------------------------------------
Define price and weight
--------------------------------------------------------------------------------
Let the price of the diamond be y and the weight be x.

--------------------------------------------------------------------------------
General equation for y varies directly as square root of x
--------------------------------------------------------------------------------
y = kx², where k is a constant

--------------------------------------------------------------------------------
Find the constant k
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when x = 12,  y = 7200
7200 = k(12)²
7200 = 144k
k = 7200 ÷ 144
k = 50

--------------------------------------------------------------------------------
Substitute k into the equation
--------------------------------------------------------------------------------
y = 50x²

--------------------------------------------------------------------------------
Calculate the weight of the two broken diamonds
--------------------------------------------------------------------------------
The diamond is broken into 3:1
3 + 1 = 4
4 shares = 12

1 share = 12 ÷ 4
1 share = 3 decigrams

3 shares = 3 x 3 
3 shares = 9 decigrams

Ratio 1 : 3 = 3 decigrams : 9 decigrams

--------------------------------------------------------------------------------
Find price of the of the 3 decigrams
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y = 50(3)²
y = $450

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Find the price of the 9 decigrams
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y = 50(9)²
y = $4050

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Total price of the 3 decigrams and the 9 decigrams
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$450 + $4050 = $4500

--------------------------------------------------------------------------------
Lost incurred
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$7200 - $4500 = $2700

--------------------------------------------------------------------------------
Answer: The lost incurred is $2700
--------------------------------------------------------------------------------

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