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Jimmy has studied 22 hours over the last 10 days for the ACT. He studied either 2 hours a day or 3 hours a day. During the 10 day period, how many days did Jimmy study for three hours a day?

User Tomaski
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Let x represent the # of 2-hour days and y the # of 3-hour days. Jimmy's study was spread over 10 days. Thus, x + y must sum up to 10. Also, 2x + 3y must sum up to 22 hours.Our system now looks like this:


x + y = 10

2x + 3y = 22


Multiply the first equation by -2: -2x - 2y = -20 Add the 2nd equation to this:


-2x - 2y = -20

2x + 3y = 22

------------------ y = 2 So Jimmy had 2 3-hour study days and 8 2-hour study days.

Note how these figures add up to 22: 6 + 16 = 22

Hope that help!

User Maxim
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