I need urgent help with these 3 math problems
1. Margaret painted a mural for St. Patrick’s Day and mixed her own green paint. She mixed 3 parts yellow paint with 2 parts blue paint to create green paint. Maureen wanted to also paint a mural with the same green color, but she currently has 8 cups of green paint that is a mixture of 40% yellow paint and 60% blue paint. To get the same shade of green as Margaret, how many cups of yellow paint must she add to her mixture?
2. Let’s now take a look at the word GREEN. There’s not too many real words that can be made from the letters in GREEN. For this problem, though, let’s see how many ways we can arrange the five letters in the word GREEN, even if they don’t form real words. But let’s also add a restriction: any arrangement must keep the two Es together. How many such arrangements are there?
3.Sunday, March 17 was St. Patrick’s Day when, typically, more people than usual wear some article of green clothing. Patrick has a leprechaun hat that looks like a tall, green top hat. The main portion of the hat is a cylinder that is 8 inches tall and has a 3-inch radius. He filled this portion of the hat with chocolates wrapped to resemble small gold coins to pass out to all his friends. One bag of these chocolate “coins” takes up about 20 in3 of space. What is the minimum number of bags of chocolate that Patrick must get to completely fill his hat?
#1 her current paint is 40% yellow, and she wants 60% yellow. So, adding x cups of yellow to the mix, we need to consider the amount of yellow paint involved.
.40*8 + 1*x = .60(8+x)
x = 4
check: she will have 12 cups, of which 3.2+7=7.2 are yellow, or 60%
So, what ideas have you on the other problems?
1. To solve this problem, we need to find out how much yellow paint Maureen needs to add to achieve the same shade of green as Margaret.
First, let's determine the total amount of paint in Maureen's current mixture. Maureen has 8 cups of green paint, which is a mixture of 40% yellow paint and 60% blue paint.
To calculate the amount of yellow paint in Maureen's mixture, we can multiply the total cups of paint by the percentage of yellow paint, which is 40%.
Yellow paint in Maureen's mixture = 8 cups * 40% = 3.2 cups
Now, let's find out the amount of blue paint in Maureen's mixture. Since the mixture is 60% blue paint, we can calculate it by multiplying the total cups of paint by the percentage of blue paint, which is 60%.
Blue paint in Maureen's mixture = 8 cups * 60% = 4.8 cups
To achieve the same shade of green as Margaret, Maureen needs to have a ratio of 3 parts yellow paint to 2 parts blue paint in her mixture.
Therefore, we need to adjust the amounts of yellow and blue paint in Maureen's mixture while maintaining the ratio of 3:2.
Let's assume Maureen needs to add x cups of yellow paint to her mixture. In this case, the ratio of yellow paint to blue paint would be (3.2 + x):(4.8).
According to the given ratio, (3.2 + x)/4.8 should be equal to 3/2.
(3.2 + x)/4.8 = 3/2
Cross-multiply to solve for x:
2(3.2 + x) = 4.8 * 3
6.4 + 2x = 14.4
2x = 14.4 - 6.4
2x = 8
x = 4
Therefore, Maureen needs to add 4 cups of yellow paint to her mixture to achieve the same shade of green as Margaret.
2. The problem asks us to find out how many ways we can arrange the five letters in the word GREEN while keeping the two Es together.
To solve this problem, we can treat the two Es as one entity. So, we will have the letters G, R, N, and EE.
Now, the total number of arrangements of these letters is equal to the factorial of the number of letters divided by the factorial of the number of repetitions (in this case, the "EE").
In this case, we have 4 distinct letters (G, R, N) and 2 repetitions ("EE").
The number of arrangements is given by:
Arrangements = 4! / 2!
Calculating this:
4! = 4 * 3 * 2 * 1 = 24
2! = 2 * 1 = 2
Arrangements = 24 / 2 = 12
Therefore, there are 12 different arrangements of the letters in the word GREEN, with the constraint of keeping the two Es together.
3. To find the minimum number of bags of chocolate that Patrick must get to completely fill his hat, we need to calculate the volume of the hat and divide it by the volume of one bag of chocolate "coins".
The hat's main portion is a cylinder with a height of 8 inches and a radius of 3 inches.
The volume of a cylinder is given by the formula:
Volume = π * radius^2 * height
Substituting the given values, we get:
Volume = π * 3^2 * 8
Volume = π * 9 * 8
Volume = π * 72
Now, let's calculate the volume of one bag of chocolate coins, which is 20 in^3.
To determine the minimum number of bags Patrick needs, we divide the volume of the hat by the volume of one bag:
Number of bags = Volume of the hat / Volume of one bag
Number of bags = (π * 72) / 20
Using an approximation of π as 3.14:
Number of bags ≈ (3.14 * 72) / 20
Number of bags ≈ 226.08 / 20
Number of bags ≈ 11.304
Since we can't have a fraction of a bag, Patrick needs to get at least 12 bags of chocolate coins to completely fill his hat.