Correct question is;
1) Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?
2) Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?
A) 0.15(40) + 0.6x = 0.25(40 + x)
B) 0.15(40) + 0.6(x – 40) = 0.25(x)
C) 0.15(40) + 0.6x = 0.25(40 – x)
D) 0.15(40) + 0.6(x + 40) = 0.25(x)
Answer:
1) Amount of cream = ¼cup
2) Option D: 0.15(40) + 0.6(x - 40) = 0.25x
Step-by-step explanation:
1) First of all, let x represent the amount of cup of milk and let y represent the of cup of cream.
We are told that the volume of the mixture is 1 cup.
Thus;
x + y = 1 - - - (eq 1)
We are now told that the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat
Thus, x contains 0.02 fat, y contains 0.18 fat and the 1 cup of mixture contains 0.06 fat.
Thus, we will multiply the respective terms in eq 1 by these %fat content.
Thus;
0.02x + 0.18y = 0.06(1)
0.02x + 0.18y = 0.06 - - - (eq 2)
From eq 1, let's make y the subject which is the amount of cup of cream.
Thus,
y = 1 - x
Let's put 1 - x for y in eq 2 to get;
0.02x + 0.18(1 - x) = 0.06
0.02x + 0.18 - 0.18x = 0.06
0.18x - 0.02x = 0.18 - 0.06
0.16x = 0.12
x = 0.12/0.16
x = 3/4 cup
From,y = 1 - x;
y = 1 - (3/4)
y = ¼ cup
Amount of cream = ¼cup
2) We are given;
15% of the pigment in paint color A is black.
60% of the pigment in paint color B is black.
We are now told that Alan unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.
If we assume the total amount of paint in the mixture is x like we are told, it means that based on the given data, we have a sum of;
0.15(40) + 0.6(x - 40)
Thus is because we know the amount of paint A used as 40 but don't know the amount of paint B used.
Now we are told that this sum produces a mixture that contains 25% black pigment. Since the total amount in the mixture is x. Thus, this final product is 0.25x.
Therefore to derive an equation to find the total amount of paint in the mixture of the two colors, we will equate the sum of the 2 Mixtures to the final product.
This gives;
0.15(40) + 0.6(x - 40) = 0.25x
