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Original Statements:
- Jared is 5 years older than Alma.
- In 9 years, the sum of their ages will be 67.
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Identify the Unknowns:
- Let’s call Alma’s current age A.
- Let’s call Jared’s current age J.
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Translate the Statements into Equations:
- “Jared is 5 years older than Alma” translates to “J = A + 5”.
- “In 9 years, the sum of their ages will be 67” translates to “(A + 9) + (J + 9) = 67”.
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Construct the Original Equations:
- We have two equations now:
- J = A + 5
- (A + 9) + (J + 9) = 67
- We have two equations now:
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Solve the Equations:
- First, substitute the value of J from the first equation into the second equation: (A + 9) + (A + 5 + 9) = 67
- Combine like terms: 2A + 23 = 67
- Subtract 23 from both sides: 2A = 44
- Divide by 2: A = 22
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Find Jared’s Age:
- Use the first equation J = A + 5 to find Jared’s age: J = 22 + 5
- J = 27
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Final Result:
- Jared is currently 27 years old.
So, Jared is 27 years old right now.