four milliliters of ink a is added to 10 milliliters of ink b, forming a mixture of inks. ink a contains 10%…

Explanation:

Step1: Calculate blue - pigment amount in ink A

The amount of ink A is 4 milliliters and it contains 10% blue pigment. So the amount of blue pigment in ink A is $4\times0.1 = 0.4$ milliliters.

Step2: Calculate total volume of the mixture

The volume of ink A is 4 milliliters and the volume of ink B is 10 milliliters. So the total volume of the mixture is $4 + 10=14$ milliliters.

Step3: Calculate total blue - pigment amount in the mixture

The mixture contains 35% blue pigment and has a volume of 14 milliliters. So the total amount of blue pigment in the mixture is $14\times0.35 = 4.9$ milliliters.

Step4: Calculate blue - pigment amount in ink B

Let the percentage of blue pigment in ink B be $x$. The amount of ink B is 10 milliliters, so the amount of blue pigment in ink B is $10x$. We know that the total blue - pigment amount in the mixture is the sum of the blue - pigment amounts in ink A and ink B. So $0.4+10x = 4.9$.

Step5: Solve for $x$

Subtract 0.4 from both sides of the equation: $10x=4.9 - 0.4=4.5$. Then divide both sides by 10: $x=\frac{4.5}{10}=0.45$ or 45%.

Answer:

45%