Question

I thought of a number, added 3 2/7 to it, then I multiplied the result by 1 1/2 , and got

6 5/7

Answer 1

`(25)/(21)`

Explanation:

First let's convert the mixed numbers into improper fractions.

`3(2)/(7)=(23)/(7)`

`1(1)/(2)=(3)/(2)`

`6(5)/(7)=(47)/(7)`

Let the number be n, so we can write an equation from the word problem as:

`(n+(23)/(7))*(3)/(2)=(47)/(7)`

Now, we do algebra and solve for n:

`(n+(23)/(7))*(3)/(2)=(47)/(7)\\(3)/(2)n+(69)/(14)=(47)/(7)\\(3)/(2)n=(47)/(7)-(69)/(14)\\(3)/(2)n=(25)/(14)\\n=((25)/(14))/((3)/(2))\\n=(25)/(14)*(2)/(3)\\n=(50)/(42)\\n=(25)/(21)`

hence the number is 25/21