Question: The sum of two numbers is 21. One number is six times the other. Find the two numbers.

The sum of two numbers is 21. One number is six times the other. Find the two numbers.

Solution

The problem states: “The sum of two numbers is 21. One number is six times the other. Find the two numbers.” Let the two numbers be \( x \) and \( y \). According to the problem, we have: \[ x + y = 21 \] and \[ x = 6y \] Substitute the expression for \( x \) from the second equation into the first equation: \[ 6y + y = 21 \] Simplify the equation: \[ 7y = 21 \] Divide both sides by 7 to solve for \( y \): \[ y = 3 \] Now, substitute the value of \( y \) back into the equation \( x = 6y \) to find \( x \): \[ x = 6 \cdot 3 \] \[ x = 18 \] The two numbers are 18 and 3.