you mix 1/3 quart of blue paint for every 1/2 quart a red paint to make 2 1/2 quarts of purple paint how much blue paint and how much red paint do you use
1/3 : 1/2 = 2:3
5/2 = 2/2 + 3/2
To find out how much blue paint and red paint are needed, we can set up a proportion based on the given ratio:
Blue paint:Red paint = 1/3 quart:1/2 quart
Let's simplify the ratio by finding a common denominator:
Blue paint:Red paint = 2/6 quart:3/6 quart
Now, we know that the total amount of purple paint required is 2 1/2 quarts. To convert the mixed fraction to an improper fraction, we multiply the whole number part (2) by the denominator (2) and add the numerator (1):
2 1/2 quarts = (2 * 2) + 1/2 = 4/2 + 1/2 = 5/2 quarts
Using the proportion, we can now determine the quantities of blue and red paint:
Blue paint = (Blue paint:Red paint) x Total purple paint
= (2/6 quart:3/6 quart) x 5/2 quarts
Canceling out common factors:
Blue paint = (2/3) x (5/2) quarts
= 10/6 quarts
= 5/3 quarts
≈ 1 2/3 quarts
Red paint = (Red paint:Blue paint) x Total purple paint
= (3/6 quart:2/6 quart) x 5/2 quarts
Canceling out common factors:
Red paint = (3/2) x (5/2) quarts
= 15/4 quarts
≈ 3 3/4 quarts
Therefore, you would need approximately 1 2/3 quarts of blue paint and 3 3/4 quarts of red paint to make 2 1/2 quarts of purple paint.
To determine how much blue paint and red paint you need to make 2 1/2 quarts of purple paint, we'll set up a proportional relationship based on the given mixing ratio.
Given that for every 1/2 quart of red paint, you mix 1/3 quart of blue paint, the ratio can be written as:
Blue paint : Red paint = 1/3 : 1/2
To find the amount of blue paint, we'll assign a variable, let's call it "x," to represent the unknown amount of blue paint. Similarly, we assign "y" to represent the amount of red paint needed.
So, we have the following equation based on the ratio:
x/y = 1/3 : 1/2
To solve this equation, we can clear the fractions by multiplying both sides by the least common multiple (LCM) of the denominators, which is 6:
6 * (x/y) = 6 * (1/3 : 1/2)
Simplifying the equation gives us:
6x/y = 2 : 3
Now, we know that the total amount of paint needed is 2 1/2 quarts, which can be expressed as 2.5 quarts.
Therefore, the equation becomes:
6x/y = 2.5
To solve for x (the amount of blue paint), we need to isolate it:
6x = 2.5y
Dividing both sides of the equation by 6:
x = (2.5y)/6
Now, we need to find a value for y (the amount of red paint) that satisfies the equation and results in 2.5 quarts of purple paint.
Since we have 2.5 quarts of purple paint, this means x (the amount of blue paint) + y (the amount of red paint) should equal 2.5:
x + y = 2.5
Substituting the value of x from the previous equation:
(2.5y)/6 + y = 2.5
Multiplying both sides by 6 to eliminate the fraction:
2.5y + 6y = 2.5 * 6
8.5y = 15
Solving for y gives:
y = 15/8.5
y ≈ 1.7647 quarts
Now, substituting this value back into the equation for x:
x = (2.5 * 1.7647)/6
x ≈ 0.7353 quarts
Therefore, to make 2 1/2 quarts of purple paint, you would need approximately 0.7353 quarts of blue paint and 1.7647 quarts of red paint.