Let's go through the problem step-by-step.
1. Identify Colin's Share:
Colin receives [tex]\(\frac{3}{10}\)[/tex] of the total money. This implies:
[tex]\[
\text{Colin's Share} = \frac{3}{10}
\][/tex]
2. Calculate the Remaining Money:
After Colin takes his share, the remaining money will be:
[tex]\[
\text{Remaining Money} = 1 - \frac{3}{10}
\][/tex]
We can simplify this:
[tex]\[
\frac{10}{10} - \frac{3}{10} = \frac{7}{10}
\][/tex]
So, the remaining money is [tex]\(\frac{7}{10}\)[/tex].
3. Share of the Remaining Money:
Emma and Dave share the remaining money in the ratio [tex]\(3:2\)[/tex]. This ratio can be divided as follows:
- Total parts in ratio = [tex]\(3 + 2 = 5\)[/tex]
- Emma's share of the remaining money = [tex]\(\frac{3}{5}\)[/tex] of [tex]\(\frac{7}{10}\)[/tex]
- Dave's share of the remaining money = [tex]\(\frac{2}{5}\)[/tex] of [tex]\(\frac{7}{10}\)[/tex]
4. Calculate Dave's Share:
To find Dave's share:
[tex]\[
\text{Dave's Share} = \frac{2}{5} \times \frac{7}{10}
\][/tex]
Multiply the fractions:
[tex]\[
\frac{2 \times 7}{5 \times 10} = \frac{14}{50} = \frac{7}{25}
\][/tex]
So, after performing all these steps, we find that Dave's share of the total money is:
[tex]\[
\boxed{0.28}
\][/tex]
