You mix 2/5 cup of red paint for every 1/4 cup of blue paint to make 1 5/8 gallons of purple paint.
a. How much red paint and blue paint do you have to use to equal 1 5/8 gallons?
b. You decide that you want to make a lighter purple paint. You make the new mixture by adding 1/10 cup of white paint for every 2/5 cup of red paint and 1/4 cup of blue paint.
How much red paint, blue paint, and white paint do you use to make 3/8 gallon of lighter purple paint?
I apologize if if doesn't make sense
a- 2/5 + 1/4=.65 mixture of red and blue paint
(2/5) / .65 X 1.625=1 gallon of red paint
(1/4) / .65 X 1.625=5/8 gllaons of blue paint, because
1 + 5/8=1 5/8 gallons of purple paint.
b-1/10 + 2/5 + 1/4=.75 mixture of white, red and blue paint
(1/10) / .75 X 3/8= 1/20 gallons of white paint
(2/5) / .75 X 3/8=1/5 gallons of red paint
(1/4) / .75 X 3/8=1/8 gallons of blue paint, because
1/20 + 1/5 + 1/8=3/8 gallons of lighter purple paint.
a. You'll have to tell how much purple paint you made/need...I think you left that part out
b Do you really add 110 cups of white paint? Is that the right number for your problem.....or a typo?
~jc
a- 2/5 + 1/4=.65 mixture of red and blue paint
(2/5) / .65 X 1.625=1 gallon of red paint
(1/4) / .65 X 1.625=5/8 gllaons of blue paint, because
1 + 5/8=1 5/8 gallons of purple paint.
b-1/10 + 2/5 + 1/4=.75 mixture of white, red and blue paint
(1/10) / .75 X 3/8= 1/20 gallons of white paint
(2/5) / .75 X 3/8=1/5 gallons of red paint
(1/4) / .75 X 3/8=1/8 gallons of blue paint, because
1/20 + 1/5 + 1/8=3/8 gallons of lighter purple paint.
a. 1 gallon equals 16 cups, so 1 5/8 gallons equals 26 cups.
solution: turn 1 5/8 into an improper fraction: (8 x 1) + 5 = 13, so 13/8
(13/8) x 16 = 26
convert:
2/5 to 8/20 cups for red
1/4 to 5/20 cups for blue
Add together.
13/20 cup equals 1 unit of purple.
red:
Divide the ratio by the whole.
(2/5 red) / (2/5 red)+(1/4 blue) =
(2/5) / (13/20) =
(2/5) x (20/13) = 8/13
(8/13) x 26 total cups = 16 cups or 1 gallon
blue:
Divide the ratio by the whole.
(1/4) / (2/5)+(1/4) =
(1/4) / (13/20) =
(1/4) x (20/13) = 5/13
(5/13) x 26 total cups = 10 cups or 10/16 of a gallon, which simplifies to 5/8 gallon.
Final answer: 1 gallon red, 5/8 gallon blue.
***
b. 1 gallon equals 16 cups, so 3/8 gallons equals 6 cups.
convert:
1/10 to 2/20 cups for white
2/5 to 8/20 cups for red
1/4 to 5/20 cups for blue
Add together.
15/20 cup or 3/4 cup equals 1 unit of light purple.
We want 6 cups of light purple so divide 6 by 3/4 equalling 8 units total.
Multiply 8 to each ratio:
1/10 white x 8/1 = 4/5 cups of white
2/5 red x 8/1 = 18/5 = 3 1/5 cups of red
1/4 blue x 8/1 = 2 cups of blue
[4/5 + 3 1/5 + 2 = 6 total cups of light purple]
A.
16 cups equal 1 gallon.
First, convert 1 5/8 gallons into cups.
1 5/8 x 16 = (13/8) x (16/1) = 26 cups
For the colors, divide each color [2/5 red and 1/4 blue] by the total of both colors [2/5 + 1/4], then multiply by the value you are determining the ratio for [26 cups].
For red:
(2/5) / (2/5)+(1/4)=
(2/5) / (13/20) =
(2/5) x (20/13)= 8/13
(8/13) x 26 = 16 cups or 1 gallon
For blue:
(1/4) / (2/5)+(1/4)=
(1/4) / (13/20) =
(1/4) x (20/13)= 5/13
(5/13) x 26 = 10 cups or 10/16 of a gallon
10/16 simplifies to 5/8 gallon
Final answer: 1 gallon of red, 5/8 gallon of blue.
