A chemist has three different acid solutions. The first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . He wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. How many liters of each solution should be used? The chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

eve and marks ratios are equivalent

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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