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Algebra Difficulty 2.5 Junior Find the answer Canada

At the end of the year 2000, Steve had $100 and Wayne had $10 000. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which year did Steve have more money than Wayne for the first time?

Pick one

Solutions — 2

Solution 1

Year	Steve	Wayne
$2000$	$\$100$	$\$10\,000$
$2001$	$\$200$	$\$5000$
$2002$	$\$400$	$\$2500$
$2003$	$\$800$	$\$1250$
$2004$	$\$1600$	$\$625$

Therefore, 2004 is the first time at which Steve has more money than Wayne at the end of the year.

Solution 2

We make a table of the total amount of money that each of Steve and Wayne have at the end of each year. After the year 2000, each entry in Steve’s column is found by doubling the previous entry and each entry in Wayne’s column is found by dividing the previous entry by 2. We stop when the entry in Steve’s column is larger than that in Wayne’s column: $\text{Year amp; Steve amp; Wayne 2000 amp; 100 amp; 10 ,000 2001 amp; 200 amp; 5000 2002 amp; 400 amp; 2500 2003 amp; 800 amp; 1250 2004 amp; 1600 amp; 625}$ Therefore, the end of 2004 is the first time at which Steve has more money than Wayne at the end of the year.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.