Question

Rodrigo practiced playing the guitar 17 1/3 hours over the past 3 weeks. He practice for 5 1/4 hours during the first week and 5 2/3 hours during the second weekhow much did rodrigo spend practicing during the third week? use the numbers and symbols to select the equation that represents the problem. then solve the equation. symbols may be used more then once 17 1/3 5 1/4 5 2/3 x = +the equation that represents the problem is A. 17 1/3 = x - 5 1/4 - 5 2/3B. x = 17 1/3 + 5 1/4 + 5 2/3 C. 17 1/3 = 5 1/4 + 5 2/3 + xD. x + 17 1/3 = 5 1/4 + 5 2/3during the third week, rodrigo spent ?/? hours practicing.

Answer 1

Since the total time of practice is 17 1/3 hours, then we can add the practice time of the three weeks to get the following equation:

`17(1)/(3)=5(1)/(4)+5(2)/(3)+x`

next,to find the number of hours of the third week, lets converte these mixed numbers into improper fractions:

`\begin{gathered} 5(1)/(4)=(21)/(4) \\ 5(2)/(3)=(17)/(3) \\ 17(1)/(3)=(52)/(3) \end{gathered}`

then, solving for x, we get:

`\begin{gathered} (52)/(3)=(21)/(4)+(17)/(3)+x \\ \Rightarrow x=(52)/(3)-(17)/(3)-(21)/(4)=(35)/(3)-(21)/(4)=(35\cdot4-21\cdot3)/(12)=(140-63)/(12)=(77)/(12)=6(5)/(12) \end{gathered}`

therefore, Rodrigo spent 6 5/12 hours practicing during the third week