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Kyle has three times as much money in his savings account as Hayden. Hayden has twice as much money in his savings account as Jeremy. Combined, Kyle, Hayden, and Jeremy have a total of [tex]$612. How much money does Kyle have in his account?
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.
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