Question

Rodrigo practiced playing the guitar 17 1/3 hours over the past 3 weeks. He practiced for 6 1/4 hours furing the firdt week snd 4 2/3 hours furing the second week. How much time did Rodrigo spend practicing during the third week? Use the number and Symbols to select the equation that represents the problem. Them solve the equation . Symbols may be used more than once or not st all..

Answer 1

let's first off, convert all mixed fractions to improper fractions, and then add.

`\bf \stackrel{mixed}{17(1)/(3)}\implies \cfrac{17\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{52}{3}} \\\\\\ \stackrel{mixed}{6(1)/(4)}\implies \cfrac{6\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{25}{4}}~\hfill \stackrel{mixed}{4(2)/(3)}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \stackrel{week~1}{6(1)/(4)}+\stackrel{week~2}{4(2)/(3)}+\stackrel{week~3}{x}=17(1)/(3)~\hfill \implies ~\hfill \cfrac{25}{4}+\cfrac{14}{3}+x=\cfrac{52}{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{25}{4}+\cfrac{14}{3}+x \right)=12\left( \cfrac{52}{3} \right)}\implies (3)25+(4)14+(12)x=(4)52 \\\\\\ 75+56+12x=208\implies 131+12x=208\implies 12x=77 \\\\\\ x=\cfrac{77}{12}\implies x=6(5)/(12)`