The second answer.
You have the first prize, x.
Then you have the second prize, which is x - 50.
Then you have the third prize, which is x - 50 -50, or x - 100.
So the total money is:
x + (x-50) + (x-100).
D because it does not specify when he would buy a house
You can simply collect terms, subtract the constant and divide by the x-coefficient. It is generally considered easier to do those steps if you eliminate fractions first (multiply by 12).
Multiply by 12
... 4(x -1) +3(x +5) = 6
... 4x -4 +3x +15 = 6 . . . . . eliminate parentheses
... 7x +11 = 6 . . . . . . . . . . . .collect terms
... 7x = -5 . . . . . . . . . . . . . . subtract the constant 11
... x = -5/7 . . . . . . . . . . . . . divide by the x-coefficient
_ _ _ _ _ _ _
Here it is the other way.
... x(1/3 +1/4) +(-1/3 +5/4) = 1/2
... (7/12)x + 11/12 = 1/2 . . add the fractions to finish collecting terms
... x + 11/7 = 6/7 . . . . . . . multiply by 12/7
... x = -5/7 . . . . . . . . . . . subtract 11/7
At the third step here, you could subtract 11/12 before doing the multiply. You get the same answer, but you have to do the extra conversion of 1/2=6/12.
