Question

I thought of a number. from ²/₇ parts of that number I subtracted 0,4 and got ⅗. The number is: A: ²⁄₇ B: ⅖ C: 3,5D: 4,5

Answer 1

Note : The use of comma as number separator represent point in this solution

Step 1: Let the number be x, thus, 2/7 parts of the number means

`(2)/(7)x`

Step 2: Subtract 0,4 from 2/7 parts of x

`(2)/(7)x-0,4\Rightarrow(2)/(7)x-(4)/(10)`

Step 3: Equate the expression above to 3/5

`(2)/(7)x-(4)/(10)=(3)/(5)`

Step 4: Simplify the equation above

`\begin{gathered} (2)/(7)x-(4)/(10)=(3)/(5) \\ (20x-28)/(70)=(3)/(5)(\text{cross multiply)} \\ 5(20x-28)=70(3) \\ 100x-140=210 \\ 100x=210+140 \\ 100x=350 \\ (100x)/(100)=(350)/(100)(\text{Divide both side by 100)} \\ x=3,5 \end{gathered}`

Hence, the number is 3,5

Option C is correct