Question

What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20

Answer 1

First, we transform the mixed fractions

`\begin{gathered} 2(1)/(4)=2+(1)/(4)=(8)/(4)+(1)/(4)=(9)/(4) \\ 1(1)/(2)=1+(1)/(2)=(2)/(2)+(1)/(2)=(3)/(2) \\ 3(3)/(5)=3+(3)/(5)=(15)/(5)+(3)/(5)=(18)/(5) \end{gathered}`

Then, we use cross multiplication

`\begin{gathered} ((9)/(4))/(x)=(9)/(4)*(1)/(x)=(9)/(4x) \\ ((5)/(2))/((18)/(5))=(3)/(2)*(5)/(18)=(15)/(36) \end{gathered}`

so, we have

`(9)/(4x)=(15)/(36)`

Finally, we solve for x, we multiply x on both sides

`\begin{gathered} (9)/(4x)x=(15)/(36)x \\ (15)/(36)x=(9)/(4) \\ x=((9)/(4))/((15)/(36)) \\ x=(9)/(4)*(36)/(15) \\ x=(9*9*4)/(15*4) \\ x=(81)/(15) \\ x=(27)/(5) \end{gathered}`

Since 27/5 = 5+2/5.Then,

`x=5(2)/(5)`

Then the answer is the second one.