The sum of two numbers is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both numbers.
M+N=25
4M-12=2N-16
the answer is 48 becouse 39+34=48
X+y=25
4x-12=2y+16
4x-2y=28
2x+2y=50
6x=78
X=13
Y=12
To find the two numbers, we'll set up a system of two equations based on the given information.
Let's call the two numbers x and y.
The first piece of information tells us that the sum of the two numbers is 25:
Equation 1: x + y = 25
The second piece of information tells us that twelve less than four times one of the numbers is 16 more than twice the other number:
Equation 2: 4x - 12 = 2y + 16
Now, we have a system of two equations:
Equation 1: x + y = 25
Equation 2: 4x - 12 = 2y + 16
To solve this system, we can use the method of substitution or elimination.
Let's use the substitution method to solve this system.
First, rearrange Equation 1 to solve for x:
x = 25 - y
Now, substitute x = 25 - y into Equation 2:
4(25 - y) - 12 = 2y + 16
Simplify Equation 2:
100 - 4y - 12 = 2y + 16
Combine like terms:
88 - 4y = 2y + 16
Add 4y to both sides and subtract 16 from both sides:
88 - 16 = 6y
Simplify:
72 = 6y
Divide both sides by 6:
y = 12
Now substitute y = 12 into Equation 1 to find x:
x + 12 = 25
Subtract 12 from both sides:
x = 13
Therefore, the two numbers are x = 13 and y = 12.