Final answer:
To find the number of red markers, the ratio of red to blue markers is used to set up an equation. The total sum of markers is given as 84, and by using the ratio 3:4, it's determined that there are 36 red markers in the art set.
Step-by-step explanation:
The question asks to determine the number of red markers given that there are 3 red markers for every 4 blue markers in an art set, with the total number of markers being 84.
To solve this, we can use the ratio of red to blue markers to set up an equation.
Let the number of red markers be R and the number of blue markers be B. The ratio can then be written as R:B = 3:4.
Given that R + B = 84, we can substitute B with 84 - R into the ratio to get a single equation with one variable.
Substituting the value of B in the ratio gives us 3:4 = R:(84-R).
Cross-multiplying yields 3(84 - R) = 4R, which simplifies to 252 - 3R = 4R, leading to 7R = 252.
Dividing both sides by 7 gives us R = 36.
Therefore, there are 36 red markers in the art set.