Ratio and Proportion

Ratio and Proportion: 0.3:2=15: X (Enter numeric value only.)

A.
100

B.
90

C.
110

D.
81

The correct answer and Explanation is :

To solve the proportion ( \frac{0.3}{2} = \frac{15}{X} ), we need to find the value of ( X ). Here’s the step-by-step process:

1. Set up the proportion: [
   \frac{0.3}{2} = \frac{15}{X}
   ]
2. Cross-multiply to eliminate the fractions: [
   0.3 \times X = 2 \times 15
   ]
3. Simplify the right side of the equation: [
   0.3 \times X = 30
   ]
4. Solve for ( X ): To isolate ( X ), divide both sides by 0.3: [
   X = \frac{30}{0.3}
   ] Performing the division: [
   \frac{30}{0.3} = 100
   ]

So, the value of ( X ) is 100.

Explanation:

Ratios and proportions are tools used to compare quantities and solve for unknown values when two ratios are set equal to each other. In this problem, we are given the proportion ( \frac{0.3}{2} = \frac{15}{X} ). To find the unknown ( X ), we use cross-multiplication, which is a standard method for solving proportions. By multiplying each side of the equation by the opposite denominator, we form an equation that is easier to solve. After solving, we find that ( X ) equals 100, which confirms that the proportions are consistent with each other.

Thus, the correct answer is:

A. 100