The price of diamond varies directly as square of its weight. The price of a 12 decigrams diamond is $7200. If diamond breaks into two pieces whose weights are in the ratio 3:1, find the loss incurred.

Question

24-03-2018
Mathematics

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The price of diamond varies directly as square of its weight. The price of a 12 decigrams diamond is $7200. If diamond breaks into two pieces whose weights are in the ratio 3:1, find the loss incurred.

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Аноним Аноним · Answer 1 · 2018-03-24T11:37:11+01:00

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Define price and weight
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Let the price of the diamond be y and the weight be x.

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

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

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Substitute k into the equation
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y = 50x²

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Calculate the weight of the two broken diamonds
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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

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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

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Lost incurred
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$7200 - $4500 = $2700

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Answer: The lost incurred is $2700
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