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As a salesperson at Trading Cards Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month he is paid $292. If he sells $900 worth of merchandise in one month he is paid $407.
Find Justins salary when he sells $3,200 worth of merchandise.
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x = monthly base pay
r = the commission as a decimal
y = the amount paid monthly
If he sells $400 worth of merchandise in one month, he is paid $292:
\[292 = x + r*400\]
If he sells $900 of merchandise in one month, he is paid $407:
\[407 = x + r*900\]
We have the following system of equations:
\[x + r*400 = 292\]
\[x + r*900 = 407\]
\[x = $200\]
r = 0.23 or 23% commission
\[y = 200 + 0.23x\]
When he sells $3,200 worth of merchandise we have x = $3,200 and we need to find y:
\[y = 200 + 0.23*3200\]
\[y = $936\]
Justin's salary when he sells $3,200 worth of merchandise is $936.
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