document.write( "Question 34488: Joanie wants to save $90 for a gift. She begins by saving $.25 the first week. Each week she saves three times as much as the week before. In how many weeks will she have saved at least $90? \n" ); document.write( "

Algebra.Com's Answer #20761 by mukhopadhyay(490) $\"\"$ $\"About$

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This forms a geometric sequence (.25, .75, 2.25,....) with initial savings as a quarter and a ratio of 3.
\n" ); document.write( "Sum of the savings must be greater than or equals $90.
\n" ); document.write( "Let the number of weeks required to save $90 is n
\n" ); document.write( "Sum = Initial[(Ratio)^n - 1]/(Ratio - 1)
\n" ); document.write( "= .25(3^n - 1)/(3-1) = .25/2 (3^n - 1);
\n" ); document.write( "We need to find minimum n for which .25/2 (3^n - 1) > = 90
\n" ); document.write( "=> (3^n - 1) >= 180/.25
\n" ); document.write( "=> (3^n - 1) >= 720
\n" ); document.write( "=> 3^n >= 721
\n" ); document.write( "3^5 = 243; 3^6 = 729;
\n" ); document.write( "Answer: 6 weeks \n" ); document.write( "

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