Question

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:
\[
\text{The numbers are } 88 \text{ and } 12.
\]