Question

Four times the sum of a number and 2/3 is 16/3.Find the number. Express your answer as a fraction in simplest form.A.) 46/3B.) 7/6C.) 2/3D.) 3/2

Answer 1

Four times the sum of a number and 2/3 can be written in the following way:

`4(x+(2)/(3))`

since this expression is equal to 16/3, we can solve for x then:

`\begin{gathered} 4(x+(2)/(3))=(16)/(3) \\ \Rightarrow4x+(8)/(3)=(16)/(3) \\ \Rightarrow4x=(16)/(3)-(8)/(3)=(8)/(3) \\ \Rightarrow x=((8)/(3))/(4)=(8)/(3\cdot4)=(8)/(12)=(2)/(3) \\ x=(2)/(3) \end{gathered}`

therefore, the missing number is 2/3