Question

2. Vernon practiced soccer 5 3/4 hours this week. He practiced 4 1/3 hours on weekdays and the rest over the weekend. a. Write an equation that represents the situation. Define your variable.b. What is the least common multiple of the denominators of 5 3/4 and 4 1/3? Show your work. c. Solve the equation and interpret the solution. Show your work.

Answer 1

a) Let x be the hours that Vernonr practice on the weekend. Then, an equation to represent this situationis:

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

b)Notice that the denominators of 5 3/4 and 4 1/3 are 4 and 3 respectively, then the least common denominator is:

`4\cdot3=12`

the LCM of 4 and 3 is 12

c)First let's convert both mixed fractions into improper fractions:

`\begin{gathered} 5(3)/(4)=(5\cdot4+3)/(4)=(20+3)/(4)=(23)/(4) \\ 4(1)/(3)=(4\cdot3+1)/(3)=(12+1)/(3)=(13)/(3) \end{gathered}`

using these improper fractions on the equation from a), we get:

`\begin{gathered} (13)/(3)+x=(23)/(4) \\ \Rightarrow x=(23)/(4)-(13)/(3)=(69-52)/(12)=(17)/(12)=1(5)/(12) \\ x=1(5)/(12) \end{gathered}`

Therefore, Vernon practiced 1 5/12 hours on the weekend