If the ratio of red marbles to green marbles is 7:3 and there are 24 green marbles, how many red marbles are there?

To determine the number of red marbles given the ratio of red to green marbles is 7:3 and there are 24 green marbles, we start by analyzing the ratio itself. The ratio tells us that for every 7 red marbles, there are 3 green marbles.

First, we can express the number of green marbles in terms of the ratio. Since the quantity of green marbles is represented by the '3' in the ratio, we can set up a proportion based on the ratio:

Let the number of red marbles be represented as ( R ).

From the ratio, we can express the relationship as:

[

\frac{R}{\text{Green}} = \frac{7}{3}

]

Substituting in the value for green marbles:

[

\frac{R}{24} = \frac{7}{3}

]

To find ( R ), we can cross-multiply:

[

R \cdot 3 = 7 \cdot 24

]

[

3R = 168

]

Now, divide both sides by 3 to obtain ( R ):

[

R = \frac{168}{3