Answer:
5 and 8.
Explanation:
Let's represent the two numbers as variables. Let x be the smaller number, and y be the larger number.
Given information:
1. The sum of the two numbers is 13: x + y = 13.
2. Five times the smaller number is 7 less than 4 times the larger number: 5x = 4y - 7.
Now, we have a system of two equations:
1. x + y = 13
2. 5x = 4y - 7
We can solve this system of equations to find the values of x and y.
First, we can rearrange equation 1 to solve for y:
y = 13 - x
Now, substitute this value of y into equation 2:
5x = 4(13 - x) - 7
Now, solve for x:
5x = 52 - 4x - 7
5x + 4x = 52 - 7
9x = 45
x = 45 / 9
x = 5
Now that we have the value of x, we can find the value of y using the first equation:
y = 13 - 5
y = 8
So, the two numbers are 5 and 8.