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Naomi has earned $54 mowing lawns the past 2 days. She worded 21/2 hours yesterday and 41/4 hourse today. If Naomi is paid the same amount for every hour she works, how much does she earn per hour to mow lawns?

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she worked 2 and 1/2 hours yesterday, and today she did 4 and 1/4 hours.

first off, let's check how many hours she worked total, and divide 54 by it.

so, first off, let's convert the mixed fractions to "improper" and add them up.


\bf \stackrel{mixed}{2(1)/(2)}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\\\ \stackrel{mixed}{4(1)/(4)}\implies \cfrac{4\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{17}{4}}\\\\ -------------------------------


\bf \cfrac{5}{2}+\cfrac{17}{4}\impliedby \textit{our LCD will be 4}\implies \cfrac{(2\cdot 5)+(1\cdot 17)}{4} \\\\\\ \cfrac{10+17}{4}\implies \cfrac{27}{4}\implies \stackrel{total~hours}{6(3)/(4)} \\\\\\ \cfrac{\stackrel{wages}{54}}{\stackrel{hours}{6(3)/(4)}}\implies \cfrac{54}{(27)/(4)}\implies \cfrac{(54)/(1)}{(27)/(4)}\implies \cfrac{54}{1}\cdot \cfrac{4}{27}\implies \cfrac{216}{27}\implies 8~(\$)/(hr)
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