I need help with a math question?

Mr. Toil is designing a symmetrical garden with 3 separate plots. A total of 12 orange flowers, 6 red flowers, and 8 yellow flowers are divided equally between garden plots A-1 and A-2. Garden plot B has 2 orange flowers, 3 red flowers, and 11 yellow flowers. Mr. Toil wants the ratio of orange flowers to the total number of flowers to be the same in each garden plot. He wants the ratio of yellow flowers to the total number in plot B to be the same as the ratio of red flowers to the total number in each of the A plots.





How many yellow flowers does he have to move from plot B to each of the A plots to achieve his goals?

I need help with a math question?
OK, let's count up the flowers There are a total of 14 orange flowers and 28 non-orange flowers in all the plots, making 42 flowers total.





Hence, for the orange/total ratio to be the same in each plot, all the plots must have twice as many non-orange flowers as orange flowers.





Plot B has 2 orange flowers. It should therefore end up with 4 non-orange flowers. That requires moving 10 yellow flowers.





Final flower distribution:


Plot B: 2 Orange 3 Red 1 Yellow


Plot A1: 6 Orange 3 Red 9 Yellow


Plot A2: 6 Orange 3 Red 9 Yellow.
Reply:you're just lazy.
Reply:This was fun to do! :P





Anyway, initially,





Plot A-1 will have :


6 orange flowers


3 red flowers


4 yellow flowers





Plot A-2 will have :


6 orange flowers


3 red flowers


4 yellow flowers





Plot B will have :


2 orange flowers


3 red flowers


11 yellow flowers





We will treat Plot A-1 and A-2 as equal because they have the same number of flowers as well as ratio.





Mr. Toil wants the ratio of orange flowers to the total number of flowers to be the same in each garden plot.





The question already states that Mr. Toil will move yellow flowers from plot B to plot A. The number of flowers however, is unknown, and will therefore be called "x". As a result of the moving of the flowers, an x amount will be added to the total amount of flowers in both Plot A-1 and A-2, whilst 2x (for two plots [A1 and A2]) will be taken away from the total in Plot B.





Therefore,





Orange flowers : to total in Plot A + x = Orange flowers : total in Plot B - 2x





6 : 13 + x = 2 : 16 - 2x


6 / 13 + x = 2 / 16 - 2x -- cross multiply to get


96 - 12x = 26 + 2x


14x = 70


x = 70/14


x = 5





Yellow flowers that need to be moved from plot B


= 2x


= 2 (5)


= 10





Check your answers.





1) Orange flowers : total in Plot A = Orange flowers : total in Plot B


6 : (13 + 5) = 2 : (16 - 10)


6 : 18 = 2 : 6


1 : 3 = 1 : 3





2) Yellow flowers : total in Plot B = red flowers to total in Plot A


(11 - 10) : (16 -10) = 3 : (13 + 5)


1 : 6 = 3 : 18


1 : 6 = 1 : 6





Hope that helped! :)