perry mixed 4 2/3 ounces of red paint and 3 1/3 ounces of yellow paint to make the right shade of orange paint. He needs 40 ounces of orange paint to paint the rest of the desk. How many ounces of red and yellow paint should Perry use to make enough orange paint to cover the top of the desk?
4 2/3 + 3 1/3 = 8 oz
Now, 40 = 8*5, so he needs 5 times as much of the paints.
Well, Perry seems to be quite the artist, or just a very dedicated desk painter! Let's crunch some numbers together, shall we?
Perry mixed a total of 4 2/3 ounces of red paint and 3 1/3 ounces of yellow paint to make the right shade of orange. If we add these amounts together, we get a total of 8 ounces of paint.
Now, if Perry needs 40 ounces of orange paint to cover the rest of the desk, we can do a little bit of math to figure out how much red and yellow paint Perry will need.
Since we know that 8 ounces of paint is made up of 4 2/3 ounces of red and 3 1/3 ounces of yellow paint, we can use that as a ratio.
To find out the ratio of how much red to how much yellow paint Perry used, we need to divide the amount of each color by the total amount of paint used (8 ounces).
So, the ratio for red paint is (4 2/3) / 8 = 0.5833, and for yellow paint it is (3 1/3) / 8 = 0.4167.
Now we can use these ratios to find out how much red and yellow paint Perry needs to make 40 ounces of orange paint.
For red paint: 0.5833 x 40 = 23.33 ounces
For yellow paint: 0.4167 x 40 = 16.67 ounces
So, Perry should use approximately 23.33 ounces of red paint and 16.67 ounces of yellow paint to make enough orange paint to cover the top of the desk.
Remember, Perry, the key to a great paint job is a steady hand and a good sense of humor. Happy painting!
To find out how much red and yellow paint Perry needs to make 40 ounces of orange paint, we'll first calculate the ratio of red to yellow paint in the mixture.
Step 1: Calculate the total ounces of paint in the mixture:
Red paint: 4 2/3 ounces
Yellow paint: 3 1/3 ounces
To add these amounts together, we convert the mixed numbers to improper fractions:
Red paint: 4 2/3 = (4 * 3 + 2) / 3 = 14/3 ounces
Yellow paint: 3 1/3 = (3 * 3 + 1) / 3 = 10/3 ounces
Adding the two amounts: 14/3 + 10/3 = (14 + 10) / 3 = 24/3 = 8 ounces
So, Perry had 8 ounces of paint in the original mixture.
Step 2: Calculate the ratio of red to yellow paint in the mixture:
Red paint: 14/3 ounces
Yellow paint: 10/3 ounces
To simplify the ratio, we divide both amounts by their greatest common divisor, which is 2:
Red paint: (14/3) ÷ 2 = 7/3 ounces
Yellow paint: (10/3) ÷ 2 = 5/3 ounces
So, the ratio of red to yellow paint in the mixture is 7/3 : 5/3.
Step 3: Calculate the proportion of red and yellow paint needed to make 40 ounces of orange paint:
Let's assume x ounces of red paint and y ounces of yellow paint are needed.
According to the ratio calculated in Step 2:
x / y = 7/3 : 5/3
To find the appropriate values for x and y, we can use cross multiplication:
3x = 7y and 3y = 5x
Now we can solve these two equations simultaneously.
Multiply the first equation by 3 and the second equation by 7 to eliminate the denominators:
9x = 21y and 21y = 35x
We can set the two right sides equal to each other to solve for x:
21y = 35x.
Rearranging the equation:
x = (21/35) * y
Step 4: Solve for x using the given amount of orange paint (40 ounces):
Substitute the calculated proportion for x in terms of y:
(21/35) * y = 40.
Simplify the equation:
21y = 35 * 40.
Divide both sides by 21:
y = (35 * 40) / 21 = 350/3 = 116 2/3.
So, Perry needs approximately 116 2/3 ounces of yellow paint.
Step 5: Calculate the amount of red paint needed:
Substitute the value of y into the equation we derived in Step 3:
x = (21/35) * (350/3) = 210/5 = 42.
Therefore, Perry needs approximately 42 ounces of red paint.
In conclusion, Perry should use approximately 42 ounces of red paint and 116 2/3 ounces of yellow paint to make enough orange paint to cover the top of the desk.
To find out how many ounces of red and yellow paint Perry should use to make enough orange paint, we need to determine the ratio of red to yellow paint in the shade of orange he made previously.
Perry mixed 4 2/3 ounces of red paint with 3 1/3 ounces of yellow paint to make the shade of orange paint. First, we need to convert these mixed numbers into improper fractions.
Converting 4 2/3 to an improper fraction:
4 * 3 = 12
12 + 2 = 14
14/3
Converting 3 1/3 to an improper fraction:
3 * 3 = 9
9 + 1 = 10
10/3
Now, let's find the total quantity of paint in the shade of orange:
14/3 ounces of red paint + 10/3 ounces of yellow paint = (14/3) + (10/3) = 24/3 = 8 ounces of orange paint.
We know that 8 ounces of orange paint is made up of 4 2/3 ounces of red paint mixed with 3 1/3 ounces of yellow paint. So, the ratio of red to yellow paint is 4 2/3 : 3 1/3, which can also be written as 14/3 : 10/3.
Now, let's calculate the amount of red and yellow paint Perry needs to make 40 ounces of orange paint for the top of the desk using this ratio.
Since the ratio is 14/3 : 10/3, we can set up the following proportion:
(red paint needed) / (yellow paint needed) = (red paint in ratio) / (yellow paint in ratio)
Let's assign variables:
Let x be the amount of red paint needed.
Let y be the amount of yellow paint needed.
We can write the equation as:
x / y = (14/3) / (10/3)
To solve for x, cross-multiply the fractions:
3x = 14 * y / 10
Next, simplify the equation:
3x = 7y / 5
To find the value of x, we need to isolate it on one side of the equation:
Multiply both sides by 5:
15x = 7y
Now, we know that Perry needs 40 ounces of orange paint to cover the top of the desk. Since the total amount of paint needed is the sum of red and yellow paint, we can set up the equation:
x + y = 40
Rearranging the equation:
y = 40 - x
Substituting this value in the previous equation:
15x = 7(40 - x)
Expanding the equation:
15x = 280 - 7x
Simplifying the equation:
15x + 7x = 280
22x = 280
Solving for x:
x = 280 / 22
x = 12.73
Rounding to the nearest whole number, Perry should use approximately 13 ounces of red paint.
Now, substituting this value in the equation y = 40 - x:
y = 40 - 13
y = 27
Therefore, Perry should use approximately 13 ounces of red paint and 27 ounces of yellow paint to make enough orange paint to cover the top of the desk.