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Let S = Sarah's annual income Let M = Mary's annual income Let x = the amount Sarah spends each year Let y = the amount Mary spends each year
Rephrased target question: What is the value of S?
Statement 1: Sarah and Mary earn an annual income in the ratio of 4:3 In other words: S/M = 4:3 Cross multiply to get 3S = 4M Simplify: 3S - 4M = 0 We can't find the value of S, so statement 1 is NOT SUFFICIENT
Statement 2: Sarah and Mary spend money in the ratio of 3:2 and together save $20,000, annually.
Sarah and Mary spend money in the ratio of 3:2 We get x/y = 3/2 Simplify to get: 2x - 3y = 0
Together they save $20,000 annually Sarah's savings + Mary's savings = 20,000 (S - x) + (M - y) = 20,000
We can't find the value of S, so statement w is NOT SUFFICIENT
Statements 1 and 2 combined: We now know that: 3S - 4M = 0 2x - 3y = 0 (S - x) + (M - y) = 20,000
Since we have 3 equations and 4 unknowns, we cannot solve this system for S. So, the combined statements are NOT SUFFICIENT
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