Answers:(A) You need to add the following to existing mixture to attain your shade:
2.125 Gallon White Paint
0.375 Gallon Blue Paint
B) Remaining 4 gallons of mixture has 2.33 Gallon water.
Explanation: A) Req. mix composition is: 5unit White + 3unit Blue = 8 units of Req mix.
We require 4 Gallon Mix = 8 units, hence each unit here is 0.5 gallon.
Therefore required final mix is :
5 x 0.5 = 2.5 Gallon White ...... (Ref i)
3 x 0.5 = 1.5 Gallon Blue. ....... (Ref ii)We currently have 1.5 Gallon of 1part White + 3part blue. So of the 4 parts of mixture we have 1 part white & 3 part blue. 1/4 White + 3/4 Blue.
Therefore white in leftover mixture = (1/4) x 1.5 gallon = 0.375 gallon
Additional white required = 2.5 - 0.375 =
2.125 gallon white .... Using 2.5 gallon from (Ref i) above
Blue in leftover mixture = (3/4) x 1.5 = 1.125 gallon
Additional white required = 1.5 -1.125 =0.375 gallon of blue paint. ... Using 1.5 gallon from (Ref ii) above.----------------------------------------------------------------------------
P.S - We know we need another 2.5 gallon paint to increase the current mix of 1.5 gallon to 4 gallon. So to speed up my calculations, I only calculated white req. and then reduced it from total of 2.5 to arrive at blue required. Hence calculations in "blue font" can be avoided. Pun intended.
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(B)Mix 1 : 2 gallon Grape juice with 1/3 water = 2 x 1/3 = 2/3 gallon water.
Mix 2 : 3 gallon Lemonade with 3/4 water = 3 x 3/4 = 9/4 gallon water.
total water in 5 gallon of final mix (mix 1 + 2) = 2/3 + 9/4 = 35/12 gallon water.
Fruit Juice in 5 gallon of final mix = 5 - (35/12) = 25/12 gallon Fruit juice
Final ratio = Fruit Juice : Water = 25/12 : 35/12 = 25 : 35 = 5:7
Now this ratio will be preserved even if some of the final mix is spilled. So after 1 gallon spill, 4 gallons of the new mix will have the same ratio; Fruit Juice : Water = 5:7 i.e. if 12 units of this mix is taken it will have 5 part Fruit juice and 7 part water. So water is 7/12 of the final mix.
7/12 of 4 gallon = (7/12) x 4 = 7/3 gallon = 2.33 gallon.
Cheers !
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