Answer to Question #325434 in Linear Algebra for maryam

Question

Ali wants to surprise his wife Sara by presenting her some flowers, when he returns back from a work tour. He plans to spend exactly $24 on a bunch of exactly two dozen flowers. Sara loves lilies, roses and daisies. At the flower market they are selling lilies for $3 each, roses for $2 each, and daisies $0.50 each. How many flowers of each type can Ali buy? 

Answer 1

Let x be the number of lilies, y be the number of roses and z be the number of daisies.

Then x+y+z = 12, and 3*x + 2*y+0.5*z = 24.

From the first equation x = 12-y-z. Substitute it in the second equation we get

36 - y - 2.5*z = 24, or y = 12 - 2.5*z. As all x, y, and z should be integer positive numbers, z can take on 2 or 4.

If z = 2 then y = 12 -5 = 7, and x = 12 -7 - 2 = 3.

If z = 4 then y = 12 - 10 = 2 and x = 12 - 2 - 4 = 6.