Solved on Feb 19, 2024

Mix black and white paint to make gray. Avery uses 5 cups black, 6 cups white. Grayson uses 4 cups black, 5 cups white. Calculate the percent of white paint to determine whose gray will be lighter.
Avery percent of white paint (to nearest whole number) $=54\%$ Grayson percent of white paint (to nearest whole number) $=56\%$ Grayson's gray paint will be lighter.

STEP 1

Assumptions
1. Avery mixes 5 cups of black paint and 6 cups of white paint.
2. Grayson mixes 4 cups of black paint and 5 cups of white paint.
3. The lightness of the gray paint is determined by the percentage of white paint in the mixture.

STEP 2

First, we need to calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = Black\, paint\, Avery + White\, paint\, Avery$

STEP 3

Now, plug in the given values for Avery's black and white paint to calculate the total amount of paint.
$Total\, paint\, Avery = 5\, cups + 6\, cups$

STEP 4

Calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = 5\, cups + 6\, cups = 11\, cups$

STEP 5

Next, we need to calculate the percentage of white paint in Avery's mixture. The percentage is calculated by dividing the amount of white paint by the total amount of paint and then multiplying by 100.
$Percentage\, white\, paint\, Avery = \left(\frac{White\, paint\, Avery}{Total\, paint\, Avery}\right) \times 100\%$

STEP 6

Plug in the values for Avery's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Avery = \left(\frac{6\, cups}{11\, cups}\right) \times 100\%$

STEP 7

Calculate the percentage of white paint in Avery's mixture.
$Percentage\, white\, paint\, Avery = \left(\frac{6}{11}\right) \times 100\% \approx 54.55\%$

STEP 8

Now, we need to calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = Black\, paint\, Grayson + White\, paint\, Grayson$

STEP 9

Now, plug in the given values for Grayson's black and white paint to calculate the total amount of paint.
$Total\, paint\, Grayson = 4\, cups + 5\, cups$

STEP 10

Calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = 4\, cups + 5\, cups = 9\, cups$

STEP 11

Next, we need to calculate the percentage of white paint in Grayson's mixture. The percentage is calculated by dividing the amount of white paint by the total amount of paint and then multiplying by 100.
$Percentage\, white\, paint\, Grayson = \left(\frac{White\, paint\, Grayson}{Total\, paint\, Grayson}\right) \times 100\%$

STEP 12

Plug in the values for Grayson's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Grayson = \left(\frac{5\, cups}{9\, cups}\right) \times 100\%$

STEP 13

Calculate the percentage of white paint in Grayson's mixture.
$Percentage\, white\, paint\, Grayson = \left(\frac{5}{9}\right) \times 100\% \approx 55.56\%$

STEP 14

Now, we compare the percentages of white paint in Avery and Grayson's mixtures to determine whose gray paint will be lighter.
- Avery's percentage of white paint: approximately 54.55% - Grayson's percentage of white paint: approximately 55.56%

STEP 15

Since the percentage of white paint determines the lightness of the gray paint, and Grayson's mixture has a higher percentage of white paint, Grayson's gray paint will be lighter.
Avery percent of white paint (to nearest whole number) $=55\%$ Grayson percent of white paint (to nearest whole number) $=56\%$ Grayson's gray paint will be lighter.

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STEP 1

Assumptions
1. Avery mixes 5 cups of black paint and 6 cups of white paint.
2. Grayson mixes 4 cups of black paint and 5 cups of white paint.
3. The lightness of the gray paint is determined by the percentage of white paint in the mixture.

STEP 2

First, we need to calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = Black\, paint\, Avery + White\, paint\, Avery$

STEP 3

Now, plug in the given values for Avery's black and white paint to calculate the total amount of paint.
$Total\, paint\, Avery = 5\, cups + 6\, cups$

STEP 4

Calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = 5\, cups + 6\, cups = 11\, cups$

STEP 5

STEP 6

Plug in the values for Avery's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Avery = \left(\frac{6\, cups}{11\, cups}\right) \times 100\%$

STEP 7

Calculate the percentage of white paint in Avery's mixture.
$Percentage\, white\, paint\, Avery = \left(\frac{6}{11}\right) \times 100\% \approx 54.55\%$

STEP 8

Now, we need to calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = Black\, paint\, Grayson + White\, paint\, Grayson$

STEP 9

Now, plug in the given values for Grayson's black and white paint to calculate the total amount of paint.
$Total\, paint\, Grayson = 4\, cups + 5\, cups$

STEP 10

Calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = 4\, cups + 5\, cups = 9\, cups$

STEP 11

STEP 12

Plug in the values for Grayson's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Grayson = \left(\frac{5\, cups}{9\, cups}\right) \times 100\%$

STEP 13

Calculate the percentage of white paint in Grayson's mixture.
$Percentage\, white\, paint\, Grayson = \left(\frac{5}{9}\right) \times 100\% \approx 55.56\%$

STEP 14

Now, we compare the percentages of white paint in Avery and Grayson's mixtures to determine whose gray paint will be lighter.
- Avery's percentage of white paint: approximately 54.55% - Grayson's percentage of white paint: approximately 55.56%

STEP 15

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STEP 1

Assumptions1. Avery mixes 5 cups of black paint and 6 cups of white paint.2. Grayson mixes 4 cups of black paint and 5 cups of white paint.3. The lightness of the gray paint is determined by the percentage of white paint in the mixture.

STEP 2

First, we need to calculate the total amount of paint Avery has mixed.Total paint Avery=Black paint Avery+White paint AveryTotal\, paint\, Avery = Black\, paint\, Avery + White\, paint\, AveryTotalpaintAvery=BlackpaintAvery+WhitepaintAvery

STEP 3

Now, plug in the given values for Avery's black and white paint to calculate the total amount of paint.Total paint Avery=5 cups+6 cupsTotal\, paint\, Avery = 5\, cups + 6\, cupsTotalpaintAvery=5cups+6cups

STEP 4

Calculate the total amount of paint Avery has mixed.Total paint Avery=5 cups+6 cups=11 cupsTotal\, paint\, Avery = 5\, cups + 6\, cups = 11\, cupsTotalpaintAvery=5cups+6cups=11cups

STEP 5

STEP 6

Plug in the values for Avery's white paint and the total paint to calculate the percentage.Percentage white paint Avery=(6 cups11 cups)×100%Percentage\, white\, paint\, Avery = \left(\frac{6\, cups}{11\, cups}\right) \times 100\%PercentagewhitepaintAvery=(11cups6cups​)×100%

STEP 7

Calculate the percentage of white paint in Avery's mixture.Percentage white paint Avery=(611)×100%≈54.55%Percentage\, white\, paint\, Avery = \left(\frac{6}{11}\right) \times 100\% \approx 54.55\%PercentagewhitepaintAvery=(116​)×100%≈54.55%

STEP 8

Now, we need to calculate the total amount of paint Grayson has mixed.Total paint Grayson=Black paint Grayson+White paint GraysonTotal\, paint\, Grayson = Black\, paint\, Grayson + White\, paint\, GraysonTotalpaintGrayson=BlackpaintGrayson+WhitepaintGrayson

STEP 9

Now, plug in the given values for Grayson's black and white paint to calculate the total amount of paint.Total paint Grayson=4 cups+5 cupsTotal\, paint\, Grayson = 4\, cups + 5\, cupsTotalpaintGrayson=4cups+5cups

STEP 10

Calculate the total amount of paint Grayson has mixed.Total paint Grayson=4 cups+5 cups=9 cupsTotal\, paint\, Grayson = 4\, cups + 5\, cups = 9\, cupsTotalpaintGrayson=4cups+5cups=9cups

STEP 11

STEP 12

Plug in the values for Grayson's white paint and the total paint to calculate the percentage.Percentage white paint Grayson=(5 cups9 cups)×100%Percentage\, white\, paint\, Grayson = \left(\frac{5\, cups}{9\, cups}\right) \times 100\%PercentagewhitepaintGrayson=(9cups5cups​)×100%

STEP 13

Calculate the percentage of white paint in Grayson's mixture.Percentage white paint Grayson=(59)×100%≈55.56%Percentage\, white\, paint\, Grayson = \left(\frac{5}{9}\right) \times 100\% \approx 55.56\%PercentagewhitepaintGrayson=(95​)×100%≈55.56%

STEP 14

Now, we compare the percentages of white paint in Avery and Grayson's mixtures to determine whose gray paint will be lighter.- Avery's percentage of white paint: approximately 54.55% - Grayson's percentage of white paint: approximately 55.56%

STEP 15

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. Avery mixes 5 cups of black paint and 6 cups of white paint.
2. Grayson mixes 4 cups of black paint and 5 cups of white paint.
3. The lightness of the gray paint is determined by the percentage of white paint in the mixture.

First, we need to calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = Black\, paint\, Avery + White\, paint\, Avery$

Now, plug in the given values for Avery's black and white paint to calculate the total amount of paint.
$Total\, paint\, Avery = 5\, cups + 6\, cups$

Calculate the total amount of paint Avery has mixed.
$Total\, paint\, Avery = 5\, cups + 6\, cups = 11\, cups$

Plug in the values for Avery's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Avery = \left(\frac{6\, cups}{11\, cups}\right) \times 100\%$

Calculate the percentage of white paint in Avery's mixture.
$Percentage\, white\, paint\, Avery = \left(\frac{6}{11}\right) \times 100\% \approx 54.55\%$

Now, we need to calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = Black\, paint\, Grayson + White\, paint\, Grayson$

Now, plug in the given values for Grayson's black and white paint to calculate the total amount of paint.
$Total\, paint\, Grayson = 4\, cups + 5\, cups$

Calculate the total amount of paint Grayson has mixed.
$Total\, paint\, Grayson = 4\, cups + 5\, cups = 9\, cups$

Plug in the values for Grayson's white paint and the total paint to calculate the percentage.
$Percentage\, white\, paint\, Grayson = \left(\frac{5\, cups}{9\, cups}\right) \times 100\%$

Calculate the percentage of white paint in Grayson's mixture.
$Percentage\, white\, paint\, Grayson = \left(\frac{5}{9}\right) \times 100\% \approx 55.56\%$

Now, we compare the percentages of white paint in Avery and Grayson's mixtures to determine whose gray paint will be lighter.
- Avery's percentage of white paint: approximately 54.55% - Grayson's percentage of white paint: approximately 55.56%