Question

Some math questions.
1. What is the value of x?
1/4x - 8 + 2/4x = 19 x = ___

2. Which expressions could complete this equation so that it has one solution?
4(4x - 3) - 6x = ___

Choose exactly two answers that are correct.

A.
12x - 12 - 2x
B.
9x - 12
C.
4x + 2 (3x - 6)
D.
4(2x + 3) - 24

3. David opens a bank account with $140 and then deposits $150 each month. Louis opens a bank account with $260 and deposits $120 each month.  How many months will it take for David and Louis to have equal amounts of money in their accounts?

A.2
  B.4
  C.5
  D.7

Answer 1

 x / 4  - 8 + 2 x /4 = 19
(1/4 + 2/4) x = 19 +8 
(3/4 ) x = 27
x = 27 * 4/3 = 9 * 4 = 36

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For the options A and C, we get    4(4x - 3) - 6x = 10 x -12
      so we get  10x = 10 x   this is true for any value of x. 

But for B and D, we get 4(4x - 3) - 6x =  9x - 12    =>   x = 0
                    4(4x - 3) - 6x = 8 x - 12        =>  x = 0    
there is one solution, x =0  for B and D.

====================

Difference between the balances in the two accounts at the beginning :
     = $ 260 - $ 140 = $ 120
Difference in the deposit amount = $ 150 - $ 120 = $ 30

So the difference in balances reduces by $ 30 each month.  So it will take $120/$30 = 4 months to even out.

Alternate method
 ============

Balance in David's account after x months = $ 140 + $ 150 * x
Balance in Louis acount after x months = $ 260 + $120 * x
 
      $ 140 + $ 150 * x =  $ 260 + $120 * x
 
         $ (150  - $120) x =   $260 - $ 140 
                 30 * x = 120
                     x = 4

Answer 2

1.

1/4x - 8 + 2/4x = 19
1/4x + 2/4x = 19 + 8
Taking x as common

( 1/4 + 2/4) x = 27
(3/4) x = 27
x= 24 × 4/3
x= 9 × 4
x = 36

2.

4(4x - 3) - 6x =

For A option 
4(4x - 3) - 6x = 12x - 12 - 2x
16x - 12 - 6x = 10x -12
10x -12 = 10x -12

For option B
4(4x - 3) - 6x = 9x - 12
16x -12 -6x = 9x -12
10x -12 =9x -12 
x = 0.

For option C.
4(4x - 3) - 6x =4x + 2 (3x - 6)
10x - 12 = 4x + 6x - 12
10x -12 =10x - 12

For option D
4(4x - 3) - 6x =4(2x + 3) - 24
10x - 12 = 8x + 12 - 24
10x -8x = -12 + 12
2x= 0
x= 0.
Hence option A and C are correct.

3.

Difference between the balances Louis   = $ 260 - $ 140 = $ 120
Difference in the deposit amount David  = $ 150 - $ 120 = $ 30

The difference in balances reduces by $ 30 each month.  So it will take $120/$30 = 4 months

Hence option B is correct.