To solve this problem, let’s use the given relationships and set up equations to find the amount of money each person has in their savings account.
1. Identify the Variables:
- Let [tex]\( J \)[/tex] represent the amount of money Jeremy has.
- Let [tex]\( H \)[/tex] represent the amount of money Hayden has.
- Let [tex]\( K \)[/tex] represent the amount of money Kyle has.
2. Set up the Relationships:
- Kyle has three times as much money as Hayden: [tex]\( K = 3H \)[/tex].
- Hayden has twice as much money as Jeremy: [tex]\( H = 2J \)[/tex].
- The total amount of money combined is [tex]$612: \( K + H + J = 612 \).
3. Substitute the Relationships into the Total Equation:
- First, substitute \( H = 2J \) into \( K = 3H \):
\[
K = 3(2J) = 6J
\]
- Now substitute \( K = 6J \) and \( H = 2J \) into the total equation:
\[
6J + 2J + J = 612
\]
- Combine like terms:
\[
9J = 612
\]
4. Solve for \( J \):
\[
J = \frac{612}{9} = 68
\]
5. Calculate \( H \) and \( K \) Using the Relationships:
- Since \( H = 2J \):
\[
H = 2 \times 68 = 136
\]
- Since \( K = 6J \):
\[
K = 6 \times 68 = 408
\]
6. Conclusion:
- Kyle has $[/tex]\[tex]$408$[/tex] in his savings account.
Thus, the answer is:
(E) [tex]\(\$ 408\)[/tex]
