Question

If ( 15 : x = 25 : 35 ), then the value of ( x ) is:

• A. 18
• B. 20
• C. 21
• D. 24

Hint:

Look at the horizontal relationship between the numerators to solve this in seconds! After simplifying the right ratio to $\frac{5}{7}$, observe that the numerator 5 is multiplied by 3 to become 15. To keep the ratio balanced, simply multiply the denominator 7 by 3 as well: $7 \times 3 = 21$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A proportion states that two ratios are completely equal to each other. When we are given a statement in the form $a : b = c : d$, it means that the fractional relationship between the first pair is structurally identical to the fractional relationship of the second pair.

Step 2: Key Formula or Approach:
The ratio expression $a : b = c : d$ can be rewritten as the fractional equation: $$\frac{a}{b} = \frac{c}{d}$$ By applying cross-multiplication, we get: $$a \times d = b \times c$$

Step 3: Detailed Explanation:
Given the proportion equation from the prompt: \[ 15 : x = 25 : 35 \] Convert the ratios into their corresponding fraction format: \[ \frac{15}{x} = \frac{25}{35} \] Before cross-multiplying, let's simplify the fraction on the right side by dividing both the numerator and denominator by their greatest common divisor, 5: \[ \frac{25}{35} = \frac{5}{7} \] Now substitute the simplified fraction back into the equation: \[ \frac{15}{x} = \frac{5}{7} \] Perform cross-multiplication to isolate the variable $x$: \[ 5 \times x = 15 \times 7 \] \[ 5x = 105 \] \[ x = \frac{105}{5} = 21 \]

Step 4: Final Answer:
The value of $x$ is 21.