Question: 8) The sum of two numbers is 15. One number is four times the other. Find the two numbers. \[ 4x…

8. The sum of two numbers is 15. One number is four times the other. Find the two numbers.

\[ 4x + y = 15 \] \[ x + 4y = 15 \]

Solution

Let’s solve the problem step by step. Step 1: Define the variables. Let \( x \) be the first number and \( y \) be the second number. Step 2: Write the equations based on the problem. The sum of the two numbers is 15: \[ x + y = 15 \] One number is four times the other: \[ x = 4y \] Step 3: Substitute the second equation into the first equation. Replace \( x \) in the first equation with \( 4y \): \[ 4y + y = 15 \] Step 4: Simplify and solve for \( y \). \[ 5y = 15 \] \[ y = 3 \] Step 5: Find \( x \) using the value of \( y \) in the second equation. \[ x = 4y \] \[ x = 4 \times 3 \] \[ x = 12 \] The two numbers are 12 and 3.