The sum of two numbers is 82. The difference is 16. What are the two numbers?
x+y=82
x-y = 16
add them to solve for x
subtract them to solve for y
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume the two numbers are x and y.
From the given information, we can write two equations:
Equation 1: x + y = 82 (the sum of two numbers is 82)
Equation 2: x - y = 16 (the difference of two numbers is 16)
Now, we can solve these equations simultaneously to find the values of x and y.
Method 1: Substitution
Let's solve Equation 1 for x:
x = 82 - y
Substitute this value in Equation 2:
82 - y - y = 16
82 - 2y = 16
Simplify:
-2y = 16 - 82
-2y = -66
Divide both sides by -2:
y = (-66) / (-2)
y = 33
Now substitute this value of y into Equation 1 to solve for x:
x + 33 = 82
x = 82 - 33
x = 49
So, the two numbers are 49 and 33.
Method 2: Elimination
Let's add the two equations together to eliminate y:
(x + y) + (x - y) = 82 + 16
2x = 98
Divide both sides by 2:
x = 98 / 2
x = 49
Now substitute this value of x into Equation 1 to solve for y:
49 + y = 82
y = 82 - 49
y = 33
So, the two numbers are 49 and 33.
To find the two numbers, we can set up a system of equations based on the given information.
Let's say the two numbers are x and y.
According to the problem, the sum of these two numbers is 82, so we can write the equation:
x + y = 82
The problem also states that the difference between the two numbers is 16, so we can write another equation:
x - y = 16
We now have a system of equations:
x + y = 82
x - y = 16
To solve this system, we can use the method of elimination. We can add the equations together to eliminate the variable y:
(x + y) + (x - y) = 82 + 16
This simplifies to:
2x = 98
To isolate x, we can divide both sides of the equation by 2:
(2x) / 2 = 98 / 2
x = 49
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
x + y = 82
49 + y = 82
Subtracting 49 from both sides:
y = 82 - 49
y = 33
Therefore, the two numbers are 49 and 33.
x + y = 82
x - y = 16
x = 82 - y
82 - y - y = 16
-2y = - 66
y = 33
x + 33 = 82
x = 49