Jia Xin and Tiffany's savings would be increased by 5% if their total savings were increased to $3280. Jia Xin's actual savings were 5% more than Tiffany's. What was the actual amount of Jia Xin's savings?
Question
Jia Xin and Tiffany's savings would be increased by 5% if their total savings were increased to $3280. Jia Xin's actual savings were 5% more than Tiffany's. What was the actual amount of Jia Xin's savings?
Solution
Let's denote the actual savings of Tiffany as T and the actual savings of Jia Xin as J.
From the problem, we know that:
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J = T + 0.05T = 1.05T (since Jia Xin's savings were 5% more than Tiffany's)
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The total savings of Jia Xin and Tiffany increased by 5%, so their actual total savings is 95% of 3280 = $3116
Now we can substitute J from the first equation into the second equation:
1.05T + T = 3116 T = 1520 (this is the actual savings of Tiffany)
Substitute T = $1520 into the first equation to find J:
J = 1.05 * 1596 (this is the actual savings of Jia Xin)
So, the actual amount of Jia Xin's savings was $1596.
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