If the ratio of two numbers is 5:6 and their difference is 11, what are the two

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Question: If the ratio of two numbers is 5:6 and their difference is 11, what are the two numbers?

Options:

Correct Answer: 25, 30

Solution:

Let the numbers be 5x and 6x. Then, 6x - 5x = 11, x = 11. The numbers are 5*11 = 55 and 6*11 = 66.

If the ratio of two numbers is 5:6 and their difference is 11, what are the two numbers?

If the ratio of two numbers is 5:6 and their difference is 11, what are the two numbers?

Step 1: Understand that the ratio 5:6 means we can represent the two numbers as 5x and 6x, where x is a common multiplier.
Step 2: Write down the two numbers: the first number is 5x and the second number is 6x.
Step 3: Use the information that the difference between the two numbers is 11. This means we can write the equation: 6x - 5x = 11.
Step 4: Simplify the equation from Step 3. This gives us: x = 11.
Step 5: Now, substitute x back into the expressions for the two numbers. For the first number: 5 * 11 = 55. For the second number: 6 * 11 = 66.
Step 6: Conclude that the two numbers are 55 and 66.

Ratios and Proportions – Understanding how to express relationships between two quantities using ratios and how to manipulate them algebraically.
Algebraic Equations – Setting up and solving equations based on given conditions, such as differences and ratios.