The difference between two numbers is 13. When the greater number is divided by the smaller, the quotient is 2 and the reminder is 5. What are the numbers?
y = x+13
y = 2x+5
Looks like x=8 and y=21
To solve this problem, we can use a system of equations.
Let's assume the smaller number is represented by x, and the greater number is represented by y.
From the given information, we can set up the following equations:
1) y - x = 13 (the difference between the two numbers is 13)
2) y = 2x + 5 (the greater number divided by the smaller number gives a quotient of 2 and a remainder of 5)
We can now solve this system of equations.
Substitute equation 2 into equation 1:
2x + 5 - x = 13
x + 5 = 13
x = 13 - 5
x = 8
Now substitute the value of x into equation 2 to find y:
y = 2 * 8 + 5
y = 16 + 5
y = 21
Therefore, the smaller number is 8 and the greater number is 21.