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Unformatted text preview: Solutions to HW #1 Math 67 UC Davis, Fall 2011 1. (a) x + y = 22 x 2 y = 7 = ⇒ x = 17 ,y = 5 (b) 4 x + 2 y = 10 2 x y = 10 = ⇒  5 = 2 x y = 10 = ⇒ no solutions (c) x + y = 10 5 x + 5 y = 50 = ⇒ x + y = 10 = ⇒ infinitely many solutions (d) x + 2 y + 3 z = 11 2 x + 6 z = 14 x + y + z = 5 = ⇒ x = 1 ,y = 2 ,z = 2 2. ... Assume that the crown was made of a mixture of gold and silver, weighed 1 pound (equal to about 454 grams) and had a volume of 30 cubic centimeters. The density of gold is known to be 19.3 grams per cubic centimeter, and the density of silver is 10.5 grams per cubic centimeter. What percentage of the crown’s weight is gold? Solution. Denote by x the weight of the gold and by y the weight of the silver, both measured in grams. The question leads to the linear system of equations x + y = 454 1 19 . 3 x + 1 10 . 5 y = 30 which can be solved to give x = 304 . 852 , y = 149 . 148 The percentage of gold is therefore x x + y = 304 . 852 454 = 0 . 67148...
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 Fall '07
 Schilling
 Math, Linear Algebra, Algebra, Centimetre gram second system of units, Konrad Zuse, bc − ad

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