Question

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?

Answer 1

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.

$\bf \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\\\ \stackrel{mixed}{4\frac{1}{4}}\implies \cfrac{4\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{17}{4}}\\\\ -------------------------------$

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