n a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is red. There are 4 cups of blue paint used in a batch of lilac paint.
a. How many cups of white paint are used?
cups
b. How many cups of red paint are used?
cups
c. How many cups of lilac paint will this batch yield?
cups
a. 40/20 * 4cups = 8 cups of white.
b. 40/20 * 4cups = 8 cups red.
c. 8 + 8 + 4 = 20 cups, total.
Let's calculate the quantities step by step:
a. To find the number of cups of white paint used, we need to calculate 40% of the total mixture. Since 40% is equivalent to 0.4, we can multiply this by the total number of cups used:
0.4 x Total number of cups = 0.4 x (Total cups of white + Total cups of blue + Total cups of red)
We know that there are 4 cups of blue paint used in the mixture. Substituting this into the equation, we get:
0.4 x Total number of cups = 0.4 x (Total cups of white + 4 + Total cups of red)
b. To find the number of cups of red paint used, we can utilize the remaining percentage, which is 100% - (40% + 20%) = 40%. Similarly, we can calculate:
0.4 x Total number of cups = 0.4 x (Total cups of white + 4 + Total cups of red)
0.4 x Total number of cups = 0.4 x (Total cups of white + Total cups of red)
c. To determine the total number of cups of lilac paint this batch will yield, we need to sum up the quantities of white, blue, and red paints:
Total Lilac Paint = Total cups of white + Total cups of blue + Total cups of red
Using the information we've calculated, we can now solve for the values of a, b, and c.
To solve this problem, we need to calculate the amount of white and red paint used in the mixture, and then determine the total amount of lilac paint that will be yielded.
a. To find the number of cups of white paint used, we first need to calculate the percentage of white paint in the mixture. Since the mixture is 40% white paint, we can use the following formula:
Number of cups of white paint = (Percentage of white paint / 100) x Total amount of paint
Plugging in the values, we get:
Number of cups of white paint = (40 / 100) x Total amount of paint
However, we don't know the total amount of paint used in the mixture. So, we need to find it. Let's assume the total amount of paint used is T cups.
Now, let's consider the amount of blue paint in the mixture. We are given that 20% of the mixture is blue, which means:
Number of cups of blue paint = (20 / 100) x T
We are given that there are 4 cups of blue paint. Therefore:
(20 / 100) x T = 4
To find T, we need to solve this equation:
0.20T = 4
Divide both sides by 0.20:
T = 4 / 0.20
T = 20
Now that we know the total amount of paint used in the mixture (T = 20 cups), we can calculate the number of cups of white paint:
Number of cups of white paint = (40 / 100) x T
= (40 / 100) x 20
= 8
Therefore, 8 cups of white paint are used.
b. To find the number of cups of red paint used, we can subtract the cups of white and blue paint from the total amount used:
Number of cups of red paint = Total amount of paint - Number of cups of white paint - Number of cups of blue paint
= 20 - 8 - 4
= 8
Therefore, 8 cups of red paint are used.
c. Finally, to find the number of cups of lilac paint that will be yielded, we can add up the cups of white, blue, and red paint:
Number of cups of lilac paint = Number of cups of white paint + Number of cups of blue paint + Number of cups of red paint
= 8 + 4 + 8
= 20
Therefore, this batch of lilac paint will yield 20 cups of paint.