The difference between two numbers is 4. The sum of the smaller number and three times the larger number is 36. What are the two numbers?
If x is the smaller, x+4 is the larger. So,
x + 3(x+4) = 36
Now just do the math ...
To solve this problem, we can set up a system of equations.
Let's assume the smaller number is represented by 'x' and the larger number is represented by 'y'.
According to the given information, the difference between two numbers is 4, so we can write the equation:
y - x = 4
The sum of the smaller number and three times the larger number is 36, which can be expressed as:
x + 3y = 36
Now, we have a system of two equations:
y - x = 4 ---(1)
x + 3y = 36 ---(2)
To solve this system, we can use the method of substitution or elimination.
Let's solve it using the substitution method.
From equation (1), we can isolate y:
y = x + 4
Now, substitute this value of y in equation (2):
x + 3(x + 4) = 36
Simplify and solve for x:
x + 3x + 12 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24/4
x = 6
Now that we have the value of x, we can substitute it back into equation (1) to find the value of y:
y - 6 = 4
y = 4 + 6
y = 10
Therefore, the two numbers are 6 and 10.