Let \( J \) represent the amount of money Jack had, and \( S \) represent the amount of money Shannon had.
According to the problem statement:
\[ 0.8J = 1.5S \]
From this, we can express \( J \) in terms of \( S \):
\[ J = \frac{1.5S}{0.8} = \frac{15S}{8} \]
Next, we need to find out how much money Jeremy had. We don't have a direct value for Jeremy's amount yet. However, we know that Mark had 50% of the combined amount of Jeremy and Shannon.
Let \( M \) represent the amount of money Mark had, and let \( R \) represent the amount of money Jeremy had. The problem states that:
\[ M = 0.5(R + S) \]
To find \( M \), we need expressions for \( R \) and \( S \).
Since we don't have additional information about \( R \), let's use the information we have to relate the amounts:
The total amount held by Jack and Shannon is:
\[ J + S = \frac{15S}{8} + S = \frac{15S}{8} + \frac{8S}{8} = \frac{23S}{8} \]
Now to express Mark's amount in terms of \( S \):
\[ M = 0.5(R + S) \]
We lack information about \( R \), but we do know \( R + S \) must somehow connect to the given condition. Suppose, for simplicity, we denote \( R \) as another variable in terms of \( S \) or finding a relation to propose a solution.
However, notice that we don't have an explicit value or ratio to use for Jeremy's amount \( R \). If we assume some reasonable conditions, let's define a particular value for Jeremy in connection to Jack and Shannon's parameters.
Now, let's assume:
If Jeremy had the same amount as Shannon:
\[ R = S \quad \text{(to simplify)} \]
Then:
\[ M = 0.5(R + S) = 0.5(S + S) = 0.5(2S) = S \]
Now keep in mind from \( 0.8J = 1.5S \), that gives \( J \) in terms of \( S \).
Finding some possible values:
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Let’s assume Shannon has some saved value. So let us portray that \( S = 80 \) as a possible value.
- Therefore, \( R = 80 \).
- Then that would yield \( J \) value as:
\[ J = \frac{15 \times 80}{8} = 150 \]
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Plugging into Mark’s formula: \[ M = 0.5(80 + 80) = 80 \]
Finally, we could say Mark has \( \text{M} = S = 80 \).
Thus, assuming crucial relations direct to equal values, the answer for Mark is:
\[ \boxed{80} \]
To validate, ensure that it satisfies conditions of ratio equality \( 0.8(150) \) should yield \( 1.5(80) \) respectively. Hence values are steered correctly, validating Mark's total as effective.