Question

the sum of two numbers is 45. one number is 4 times as large as the other. what are the numbers?
larger number:
smaller number:

Explanation:

Step1: Define variables

Let the smaller number be \( x \). Then the larger number is \( 4x \) (since it's 4 times the smaller one).

Step2: Set up equation

The sum of the two numbers is 45, so we have the equation \( x + 4x = 45 \).

Step3: Solve for \( x \)

Combine like terms: \( 5x = 45 \). Then divide both sides by 5: \( x = \frac{45}{5} = 9 \).

Step4: Find the larger number

The larger number is \( 4x = 4\times9 = 36 \).

Answer:

Larger number: 36
Smaller number: 9