Question

What must be added to each term of the ratio 2 : 5 so that it may equal to 5 : 6?

• A. 12
• B. 13
• C. 15
• D. 14

Answer 1

Answer:

B. 13

Understanding Ratios and Proportions

• A ratio is a comparison of two quantities of the same kind. It is expressed as a : b or a/b.

• A proportion is an equality between two ratios. If a : b = c : d, then ad = bc (product of extremes equals product of means).

Problem-Solving Steps

1. Represent the Unknown: Let the number that must be added to each term of the ratio be x.

2. Formulate the New Ratio: The initial ratio is 2 : 5. After adding x to each term, the new ratio becomes (2 + x) : (5 + x). This can also be written as a fraction: (2 + x) / (5 + x).

3. Set up the Proportion: The problem states that this new ratio should be equal to 5 : 6. Therefore, we set up the equation:(2 + x) / (5 + x) = 5 / 6

4. Solve for x using Cross-Multiplication: Cross-multiplication is a method used to solve equations involving fractions. You multiply the numerator of one fraction by the denominator of the other fraction and set them equal.

   • 6 * (2 + x) = 5 * (5 + x)

   • Distribute the numbers on both sides:12 + 6x = 25 + 5x

5. Isolate x: To find the value of x, gather all terms with x on one side and constant terms on the other side.

   • Subtract 5x from both sides:12 + 6x - 5x = 2512 + x = 25

   • Subtract 12 from both sides:x = 25 - 12x = 13