How much money ?
During the first week of their vacation trip, the Gomez family spent $200 more than three fifths of their vacation money and had more than $400 less than half of it left. If they started their trip with a whole number of dollars, what was the greatest amount of vacation money they could have had?
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1 solution
Let M = money they started with.
"During the first week of their vacation trip, the Gomez family spent $200 more than three fifths of their vacation money"
First week spending = 3/5 M + 200, leaving M - 3/5 M - 200 or 2/5 M - 200. "had more than $400 less than half of it left." 2/5 M - 200 > M/2-400 Add 400 2/5 M + 200 > M/2 Convert to common denominator 4/10 M + 200 > 5/10 M Subtract 4/10 M 200 > 1/10 M Mult by 10 2000 > M The most they could have started with was $1999