Ben had some marbles. The number of blue marbles was $\frac{1}{2}$ the number of red marbles. The number of red marbles was $\frac{4}{5}$ the number of green marbles.

1. Express the given relationships as ratios

Blue : Red = $1 : 2$
Red : Green = $4 : 5$

2. Make the common term (Red) equal in both ratios

Blue : Red = $1 : 2 = 2 : 4$
Red : Green = $4 : 5$

3. Combine into a single ratio

Blue : Red : Green = $2 : 4 : 5$

1. Determine the ratio of blue, red, and green marbles from part (a)

From part (a), the ratio of Blue : Red : Green is $2 : 4 : 5$.

2. Find the total number of units for blue and green marbles

Blue units = $2$
Green units = $5$
Total units for blue and green = $2 + 5 = 7$ units

3. Calculate the value of 1 unit

$7$ units = $42$
$1$ unit = $42 \div 7 = 6$

4. Calculate the number of red marbles

Red units = $4$
Number of red marbles = $4 \times 6 = 24$