<p>Tom and Alison are both salespeople. Toms weekly
compensation consists of $300 plus 20 percent of his
sales. Alisons weekly compensation consists of $200
plus 25 percent of her sales. If they both had the same
amount of sales and the same compensation for a
particular week, what was that compensation, in
dollars? (Disregard the dollar sign when gridding).</p>
<p>~ I thought this was an easy problem but I got it wrong apparently. From 2009-10 CB SAT.</p>
<p>if t is the sales for tom and a the sales for alison, then you are trying to find the solutions for: 300+0.2t=200+0.25a
and a=t
thus: 300+0.2t=200+0.25t
100=0.05t
t=100/0.05=2000
compensation= 300+0.2<em>2000=700
check: 200+0.25</em>2000=700</p>
<p>You could think of it this way:</p>
<p>Allison starts $100 behind, but makes 5% more than Tom in commissions.</p>
<p>5% is 1/20th, so when sales are $2000, she will have made up the $100 deficit.</p>
<p>Allison compensation $200 plus 25% of $2000 makes $700</p>
<p>checking: Tom compensation $300 plus 20% of $2000 makes $700</p>