The sum of 2 number is 100. When the greater number is divided by the lesser, the partial quotient is 7 and the remainder is 4. Find the numbers.

Answer 1

Let's denote the two numbers as \( x \) (greater number) and \( y \) (lesser number). According to the problem, we have the following relationships:

1. The sum of the two numbers: \[ x + y = 100 \]

2. When the greater number is divided by the lesser number, the partial quotient is 7 and the remainder is 4: \[ x = 7y + 4 \]

Now, we can use these two equations to solve for \( x \) and \( y \).

Step 1: Substitute the second equation into the first

Substituting \( x \) from the second equation into the first equation: \[ (7y + 4) + y = 100 \]

Step 2: Simplify the equation

Combine like terms: \[ 7y + y + 4 = 100 \] \[ 8y + 4 = 100 \]

Step 3: Solve for \( y \)

Subtract 4 from both sides: \[ 8y = 96 \]

Now, divide by 8: \[ y = 12 \]

Step 4: Solve for \( x \)

Now that we have \( y \), substitute it back to find \( x \): \[ x = 100 - y = 100 - 12 = 88 \]

Conclusion

The two numbers are: \[ x = 88 \quad \text{(greater number)} \] \[ y = 12 \quad \text{(lesser number)} \]

Thus, the final answer is: \[ \text{The numbers are } 88 \text{ and } 12. \]