Ratio and Proportion: 200:2 = 20: X (Enter numeric value only.)
A.
0.2
B.
2
C.
0.1
D.
3
The Correct answer and Explanation is:
To solve the ratio and proportion problem 2002=20X\frac{200}{2} = \frac{20}{X}2200=X20, follow these steps:
- Set Up the Proportion: We start with the given proportion:2002=20X\frac{200}{2} = \frac{20}{X}2200=X20This proportion states that the ratio of 200 to 2 is equal to the ratio of 20 to XXX.
- Simplify the Known Ratio: First, simplify the left side of the proportion:2002=100\frac{200}{2} = 1002200=100So, our proportion now looks like:100=20X100 = \frac{20}{X}100=X20
- Solve for XXX: To find XXX, cross-multiply and solve the resulting equation. Cross-multiplying involves multiplying the numerator of one ratio by the denominator of the other ratio:100×X=20×1100 \times X = 20 \times 1100×X=20×1Simplify this to:100X=20100X = 20100X=20Next, solve for XXX by dividing both sides by 100:X=20100=0.2X = \frac{20}{100} = 0.2X=10020=0.2
- Verify the Answer: To ensure accuracy, substitute X=0.2X = 0.2X=0.2 back into the original proportion:2002=200.2\frac{200}{2} = \frac{20}{0.2}2200=0.220Simplify 200.2\frac{20}{0.2}0.220:200.2=100\frac{20}{0.2} = 1000.220=100Since both sides are equal, our solution is confirmed.
Thus, the correct answer is 0.2\boxed{0.2}0.2, which corresponds to option A.