If the ratio of two numbers is 7:9 and their sum is 80, what is the larger numbe

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Question: If the ratio of two numbers is 7:9 and their sum is 80, what is the larger number?

Options:

Correct Answer: 45

Solution:

Let the numbers be 7x and 9x. Then, 7x + 9x = 80, 16x = 80, x = 5. Larger number = 9x = 9*5 = 45.

If the ratio of two numbers is 7:9 and their sum is 80, what is the larger number?

If the ratio of two numbers is 7:9 and their sum is 80, what is the larger number?

Step 1: Understand that the ratio of the two numbers is 7:9. This means if we call the first number '7x', the second number will be '9x'.
Step 2: Write down the equation for their sum. Since the sum of the two numbers is 80, we can write: 7x + 9x = 80.
Step 3: Combine the terms on the left side of the equation. This gives us: 16x = 80.
Step 4: Solve for 'x' by dividing both sides of the equation by 16. So, x = 80 / 16.
Step 5: Calculate the value of 'x'. This gives us x = 5.
Step 6: Now, find the larger number. Since the larger number is represented by '9x', we calculate: 9 * 5.
Step 7: Perform the multiplication to find the larger number. This gives us 45.

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.