N+M=120
M-4N=15
solve for n, m.
M-4N=15
solve for n, m.
We know that the sum of the two numbers is 120, so we can write the equation:
x + y = 120 -- (Equation 1)
We also know that when four times the smaller number is subtracted from the larger number, the result is 15. Mathematically, we can express this as:
y - 4x = 15 -- (Equation 2)
Now, we have two equations with two variables. We can use any method like substitution or elimination to solve for x and y.
Let's use the substitution method:
1. Solve Equation 1 for y:
y = 120 - x
2. Substitute this value of y into Equation 2:
120 - x - 4x = 15
3. Simplify the equation by combining like terms:
120 - 5x = 15
4. Move the constant term to the other side:
-5x = 15 - 120
5. Simplify further:
-5x = -105
6. Divide both sides of the equation by -5 to solve for x:
x = -105 / -5
x = 21
Now that we have found the value of x, we can substitute it back into Equation 1 to find y:
y = 120 - x
y = 120 - 21
y = 99
Therefore, the two numbers are 21 and 99.