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

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

If the ratio of two numbers is 7:9 and their sum is 80, what is the smaller 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 smaller number by substituting 'x' back into the expression for the smaller number, which is 7x. So, 7 * 5 = 35.
Step 7: Conclude that the smaller number is 35.

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