If one-half of a number is 8 less than two thirds of the number what is the number A) 24 B)32 C) 48 D)54?

Answer 1

C

1/2 of x is 2/3 of x minus 8

(1/2)x = (2/3)x -8

clear fraction by multiplying by 6

3x = 4x -48

x = 48

Answer 2

Question:
If one-half of a number is 8 less than two thirds of the number what is the number?
A) 24
B) 32
C) 48
D) 54

The Information Given:
Let break down the information.
• Let “x” be the number.
• “…one-half of a number is 8…” or x/2 = 8
• “…8 less than two thirds of the number..” or 2/3x – 8
• Now combine these 2 equations. x/2 = 2/3x – 8.

Solution Process:
• Step 1: Write down your equation
• x/2 = 2/3x – 8
• Step 2: Get your variables (x) on one side by subtracting one of the variables (x) so they cancel out.
• x/2-2/3x = 2/3x-2/3-8
• Step 3: Simplify:
• -x/6 = -8
• Step 4: To get x alone multiply by the reciprocal.
• -x/6 ∙ -6 = -8 ∙ -6
• Step 5: Simplify to get your answer.
• x = 48


Why It Is Correct:
If you plug in 48 for x you should the sides to equal.
 x/2 = 2/3x – 8
 48/2 = 2/3(48) -8
 24 = 32 – 8
 24 = 24 (correct)

Strategies That Could Used:
 Plug in the answer
 Use Algebra
 Wild Guess
 Skip the Question

Answer 3

Answer is C
Let the number be x
x/2 = 2x/3 - 8
2x/3 - x/2 = 8
Taking LCD
(4x-3x)/6 = 8
x/6 = 8
x= 48

Answer 4

sol'n:
let x=number
interpretting the problem:
(1/2)x = (2/3)x - 8
by tranposing similar terms,
8= (2/3)x - (1/2)x
find the LCD,
8 = (4x-3x)/6,
8 = x/6 then multiply both sides by 6,
(8 = x/6)(6), we get
48 = x...

therefore, the number is 48...

Answer 5

Let X be the number.
one half of X is X/2
2/3 of the number is 2X/3
X/2= 2X/3-8
solve for X
multiply both sides by 6
3X=4X-48
-X=-48
X=48
(C)

Answer 6

x/2=(2x/3)- 8

=>x=48

Answer 7

let number be x
(2/3)x - 8 = (1/2) x
4x - 48 = 3x
x = 48
OPTION C

Answer 8

let "x" be the no.
x/2 = 2x/3 - 8
2x/3 -x/2 = 8
(4x - 3x)/6 = 8
x/6 = 8
x = 48

ANS = C