If the ratio of two numbers is 7:9 and their sum is 128, what is the larger numb

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Question: If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?

Options:

Correct Answer: 72

Solution:

Let the numbers be 7x and 9x. Then, 7x + 9x = 128, 16x = 128, x = 8. Larger number = 9x = 9*8 = 72.

If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?

If the ratio of two numbers is 7:9 and their sum is 128, what is the larger number?

Step 1: Understand that the ratio 7:9 means for every 7 parts of the first number, there are 9 parts of the second number.
Step 2: Let the first number be 7x and the second number be 9x, where x is a common multiplier.
Step 3: Write the equation for their sum: 7x + 9x = 128.
Step 4: Combine the terms on the left side: 16x = 128.
Step 5: Solve for x by dividing both sides by 16: x = 128 / 16.
Step 6: Calculate x: x = 8.
Step 7: Find the larger number by calculating 9x: Larger number = 9 * 8.
Step 8: Calculate the larger number: Larger number = 72.

Ratios – Understanding and applying the concept of ratios to express relationships between two quantities.
Algebraic Manipulation – Using algebra to solve for unknowns by setting up equations based on given relationships.
Word Problems – Translating a word problem into mathematical expressions and equations.