Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s).
The sum of two numbers is 36. Their difference is 4. Determine the two unknown numbers.
Solve this the same way I showed you earlier.
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First case:
x+y =36... equation (i )
Second case:
x-y =4 ......equation (ii)
Solving equation i and ii by eliminating method we get,
x+y = 36
x-y =4
2x =40
x = 40÷2
.: x = 20
Now, putting the value of x in equation i we get,
20 + y = 36
y = 36-20
.: y=16
To solve this problem, we need to set up an equation based on the given information. Let's assume that the first number is represented by 'x' and the second number is represented by 'y'.
According to the given information, the sum of the two numbers is 36. Therefore, the equation can be written as:
x + y = 36 ...(Equation 1)
The second piece of information states that the difference between the two numbers is 4, which means that the larger number minus the smaller number is equal to 4. So, the equation can be written as:
x - y = 4 ...(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution for this example.
First, rearrange Equation 1 to solve for one variable:
x + y = 36
x = 36 - y ...(Equation 3)
Next, substitute the value of x from Equation 3 into Equation 2:
(36 - y) - y = 4
Simplify the equation:
36 - 2y = 4
Now, isolate the variable 'y' by moving constant terms to the other side:
-2y = 4 - 36
-2y = -32
Divide both sides by -2 to solve for 'y':
y = -32 / -2
y = 16
Now, substitute the value of y into Equation 3 to solve for 'x':
x = 36 - y
x = 36 - 16
x = 20
So, the two unknown numbers are 20 and 16.