The ratio of Agnes to John's savings was 4 : 5 at first. After Agnes saved another $170 and John saved another $31, Agnes had twice of John. How much did Agnes have in the end
Question
The ratio of Agnes to John's savings was 4 : 5 at first. After Agnes saved another 31, Agnes had twice of John. How much did Agnes have in the end
Solution
Let's denote Agnes's initial savings as 4x and John's initial savings as 5x.
After Agnes saved another $170, her total savings became: 4x + 170
After John saved another $31, his total savings became: 5x + 31
According to the problem, Agnes's savings at this point were twice John's savings: 4x + 170 = 2(5x + 31)
Now, let's solve this equation step by step:
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Expand the right side of the equation: 4x + 170 = 10x + 62
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Subtract 4x from both sides to isolate the variable term on one side: 170 = 6x + 62
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Subtract 62 from both sides to further isolate the variable term: 108 = 6x
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Divide both sides by 6 to solve for x: x = 18
Now, we can find Agnes's initial savings: 4x = 4 * 18 = 72
After saving another $170, Agnes's total savings became: 72 + 170 = 242
Therefore, Agnes had $242 in the end.
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