The ratio of x to y is 1/2.If the ratio of x+2 to y+1 is 2/3, then what is the value of x?

To understand why the answer is 4, let's break down the problem step by step.

We start with the first piece of information that the ratio of x to y is 1/2. This can be written as:

• x/y = 1/2

This implies that:

• x = 1/2 * y

Next, we have the second ratio given, which is the ratio of (x + 2) to (y + 1) being 2/3:

• (x + 2)/(y + 1) = 2/3

Cross-multiplying gives us:

• 3(x + 2) = 2(y + 1)

Expanding both sides, we get:

• 3x + 6 = 2y + 2

Now, we can substitute the value of y in terms of x from the first equation:

• y = 2x

Substituting this into the equation we derived:

• 3x + 6 = 2(2x) + 2

This simplifies to:

• 3x + 6 = 4x + 2

Rearranging the equation, we can solve for x:

• 3x - 4x = 2 - 6
• -x = -4
• x = 4

Thus, the value of x is 4, which is why the answer is correct.

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