Question

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?

A) 6
B) 4
C) 3
D) 2
E) 1

Answer 1

By setting up equations based on the given ratios and solving for x, we conclude that the value of x is 4, option B.

Step-by-step explanation:

To determine the value of x, we must use the given ratios to set up two separate equations and then solve for x. We are given that the ratio of x to y is 1/2 and that the ratio of x + 2 to y + 1 is 2/3. With the data at hand, we can construct two equations:

We can express y in terms of x using the first equation: y = 2x. When we replace this in the second equation, we obtain:

(x + 2)/(2x + 1) = 2/3

Multiplying both sides by (2x + 1) to eliminate the denominator, we get:

3(x + 2) = 2(2x + 1)

Expanding and simplifying, we obtain:

3x + 6 = 4x + 2

Subtracting 3x from both sides:

6 = x + 2

Finally, solving for x we get:

x = 4, which corresponds to answer choice B.