Three times the sum of a number and 4 is the same as 8 less than one-half the number. What is the value of the number?

Question

hard af soooooooooooooo hard

Answer 1

Hi, this story problem is not so hard if you first write it and underline the key words.  For example, let me work a problem similar to this one:   Three times (the sum of a number and 10) is the same as 4 less than one-half the number.  What is the value of the number?  Just work your problem just like the one below:  

 

Sum means add.                Times means multiply.     "Is the same as means ="           

"Less" in this case means subtraction.

 

Now     Let x= the number             Then   3( x +10)= (1/2)X— 4    Use Distributive Property

            3x +30 = x — 4         Multiply every term by reciprocal of  (1/2) which is 2/1

                            2

          2(3x) + 2(30) = 2 (1/2)x - 2(4)→ 6x + 60= X — 8           2/2 =1        (2/2)x= 1x=x

 Subtract the smaller "1x" from both sides of equation.

   6x-x+60=x-x-8  →  5x+60= -8   Solve for "x."  Simplify by getting rid of "60" to get 5x by itself.

    5x+60-60=-8-60            -60=+-60        5x=-8+ -60=-68    5x=-68    Divide by number next to 5x, which is "5."      5/5 x = -68/5      x=-68/5=-13.6 using a calculator   This problem can be checked by substitution of the -13.6 into the original setup.     3(x+10)= (1/2)x -4      3(-13.6+10)= (1/2)((-13.6) -4        3(-3.6)=.5(-13.6)-4

                                                                                   -10.8=-6.8-4=-10.8   Therefore, x=-13.6

                                        Thank you,   Susan C.