Question

If 36: 84 :: 42: X, then the value of X, is:

• A. 18
• B. 98
• C. 72
• D. 48

Hint:

In proportion problems, you can also simplify the first ratio before solving. \(36:84\) can be simplified by dividing both numbers by their greatest common divisor, which is 12. \(36 \div 12 = 3\) and \(84 \div 12 = 7\). So the proportion becomes \(3:7 :: 42:X\). Now, \(3 \times X = 7 \times 42\), which gives \(X = (7 \times 42) / 3 = 7 \times 14 = 98\).

Answer 1

The Correct Option is B

Step 1: Understanding Proportions:
A proportion of the form a: b :: c: d states that the product of the extremes (a and d) equals the product of the means (b and c). Mathematically, this is represented as \(a \times d = b \times c\).

Step 2: Applying the Proportion Rule:
The given proportion is \(36: 84 :: 42: X\). Identifying the terms: a = 36, b = 84, c = 42, and d = X. Applying the proportion rule yields: \[ 36 \times X = 84 \times 42 \]
Step 3: Solving for X:
To determine the value of X, solve the equation derived in Step 2: \[ 36 \times X = 84 \times 42 \] Isolate X: \[ X = \frac{84 \times 42}{36} \] Simplify the fraction by factoring: \(42 = 6 \times 7\) and \(36 = 6 \times 6\). \[ X = \frac{84 \times (6 \times 7)}{6 \times 6} \] Cancel one factor of 6 from the numerator and denominator: \[ X = \frac{84 \times 7}{6} \] Divide 84 by 6: \(84 \div 6 = 14\). \[ X = 14 \times 7 \] \[ X = 98 \]
Step 4: Conclusion:
The calculated value for X is 98.