Question

four milliliters of ink a is added to 10 milliliters of ink b, forming a mixture of inks. ink a contains 10% blue pigment. ink b contains an unknown percentage of blue pigment. the mixture of the two inks contains 35% blue pigment. what percentage of blue pigment is in ink b?
○ 45%
○ 40%
○ 60%
○ 75%

Explanation:

Step1: Define variables

Let \( x \) be the percentage of blue pigment in ink B (in decimal form, so if it's \( p\% \), \( x=\frac{p}{100} \)). The volume of ink A is \( 4 \) mL with \( 10\% = 0.1 \) blue pigment, volume of ink B is \( 10 \) mL with \( x \) blue pigment, and the mixture volume is \( 4 + 10=14 \) mL with \( 35\% = 0.35 \) blue pigment.

Step2: Set up the equation

The amount of blue pigment in ink A plus the amount in ink B equals the amount in the mixture. So, \( 4\times0.1+10\times x = 14\times0.35 \).

Step3: Solve the equation

First, calculate the left and right sides: \( 0.4 + 10x=4.9 \). Then, subtract \( 0.4 \) from both sides: \( 10x = 4.9 - 0.4=4.5 \). Then, divide both sides by \( 10 \): \( x = 0.45 \). To convert to percentage, multiply by \( 100 \), so \( 45\% \).

Answer:

45% (corresponding to the option "45%")