The sum of two numbers is 100. If four times the smaller number is subtracted from the larger number, the result is 10. Find the two numbers.

1. Problem Description

The sum of two numbers is

1

0

0. If four times the smaller number is subtracted from the larger number, the result is

1

0. Find the two numbers.

2. Solution Steps

Let $x$ be the larger number and $y$ be the smaller number.

We can set up two equations based on the given information:

$x + y = 100$ (The sum of two numbers is 100)

$x - 4y = 10$ (If four times the smaller number is subtracted from the larger number, the result is 10)

We can solve this system of equations. From the first equation, we can express $x$ in terms of $y$:

$x = 100 - y$

Substitute this expression for $x$ into the second equation:

$(100 - y) - 4y = 10$

$100 - 5y = 10$

$-5y = 10 - 100$

$-5y = -90$

$y = \frac{-90}{-5}$

$y = 18$

Now, substitute the value of $y$ back into the expression for $x$:

$x = 100 - y = 100 - 18 = 82$

So, the larger number is 82 and the smaller number is

1

8.

3. Final Answer

The larger number is

8

2. The smaller number is 18.