Ratio and Proportion: 0.5:20:: X: 200

Ratio and Proportion: 0.5:20:: X: 200

A.
X=5

B.
X=50

C.
X=4

D.
X=25

To solve the ratio and proportion problem 0.5:20::X:2000.5 : 20 :: X : 2000.5:20::X:200, follow these steps:

1. Understand the Proportion: The given proportion can be written as:0.520=X200\frac{0.5}{20} = \frac{X}{200}200.5​=200X​This equation states that the ratio of 0.5 to 20 is equal to the ratio of XXX to 200. We need to find XXX that maintains this equality.
2. Cross-Multiply to Solve for XXX: To solve for XXX, cross-multiply the terms in the proportion:0.5×200=20×X0.5 \times 200 = 20 \times X0.5×200=20×XSimplify the left side:0.5×200=1000.5 \times 200 = 1000.5×200=100So, the equation becomes:100=20×X100 = 20 \times X100=20×X
3. Solve for XXX: To isolate XXX, divide both sides of the equation by 20:X=10020=5X = \frac{100}{20} = 5X=20100​=5

Thus, the value of XXX that satisfies the proportion is 555.

Explanation: Ratios and proportions are fundamental concepts in mathematics used to compare quantities. A ratio is a way to express how one quantity relates to another, and a proportion states that two ratios are equal. When solving proportion problems, we often use cross-multiplication to find the unknown value.

In this problem, the proportion 0.5:20::X:2000.5 : 20 :: X : 2000.5:20::X:200 is solved by setting up an equation where the two ratios are equal. By cross-multiplying, we form an equation that allows us to isolate the unknown variable XXX. Solving this equation involves basic algebraic operations, demonstrating the relationship between the quantities in the proportion.

The correct answer is:

A. X = 5