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Question

If three times a number, is added to 4 is divided by the number plus 3, the result is five halves. find the number

Answer 1

Problem

If three times a number, is added to 4 is divided by the number plus 3, the result is five halves. find the number

Step 1

We start by writing an equation which represents the problem to be solved.

We will call the unknown number x

We're told that three times x is added to four.  3x + 4

And this is to be divided by  x + 3

And we know the answer is going to be  5/2

So the complete statement of the problem is this:

  3x + 4 = 5

    x + 3    2

Step 2

Let's multiply both sides of the equation by x + 3

        (x + 3) • 3x + 4 = 5 • (x + 3)

                 x + 3   2

The x + 3’s on the left side cancel out because x + 3 over x + 3 equals 1

We are left with 3x + 4 on the left.

Multiplying the right side by x + 3 results in 5x + 15 divided by 2.

It looks like this:

3x + 4 = 5x + 15

                 2

Step 3 

Multiplying both sides by 2 gives us the result:

6x + 8 = 5x +15   (The 2’s cancel out on the right side)

Step 4 

Now combine the terms, the x’s on the left and the numbers on the right.

That means subtract 5x from both sides, and subtract 8 from both sides, with this result:

(6x - 5x ) = (15 - 8 ) which reduces to  x = 7

So the number we are looking for is 7

Step 5

Let’s check it by plugging 7 into the original equation

(3 • 7) + 4 = 25 

  (7 + 3)    10

Now we can divide by the common factor of 5 and the result is 5/2 Voila!

Answer 2

x = the number

3x + 4 5

--------- = -----

x + 3 2

6x + 8 = 5x + 15

x = 7