some number was divided into 176.9. this quotient was then multiplied by 4 , after which the resulting product was added to 10.2 given this sum totalled -38.6, find the initial number

9514 1404 393

  -14.5

Step-by-step explanation:

Let the number be represented by x.

  176.9/x . . . . the quotient of some number divided into 176.9

  4(176.9/x) . . . . the quotient multiplied by 4

  10.2 + 4(176.9/x) . . . . the product added to 10.2

And that totals -38.6:

  -38.6 = 10.2 +4(176.9/x)

Solution

  -48.8 = 4(176.9/x) . . . . subtract 10.2

  -12.2 = 176.9/x . . . . . . . divide by 4

  x = 176.9/(-12.2) . . . . . multiply by x/-12.2

  x = -14.5 . . . . . . . . . . . finish the division

The initial number is -14.5.