The sum of two numbers is 38. Their difference is 12. What are the two numbers?
Solve this pair of equations:
x + y = 38
x - y = 12
If you are familiar with algebra, you will see right away that 2x = 50. x is the larger of the two numbers
25 13
:D
Let's solve the problem step by step:
Step 1: Assign variables to the unknown numbers.
Let's call the first number x and the second number y.
Step 2: Translate the given information into equations.
The sum of two numbers is 38, so we have the equation: x + y = 38.
Their difference is 12, so we have another equation: x - y = 12.
Step 3: Solve the system of equations.
To solve the system of equations, we can use the method of substitution or elimination.
We'll use the method of elimination to solve this system:
Multiply the second equation by -1 to change the signs:
-x + y = -12.
Now, add the two equations:
(x + y) + (-x + y) = 38 + (-12)
2y = 26
Step 4: Solve for y.
Divide both sides of the equation by 2:
y = 13
Step 5: Substitute the value of y into one of the original equations to solve for x.
Using the equation x + y = 38, substitute the value y = 13:
x + 13 = 38
Step 6: Solve for x.
Subtract 13 from both sides of the equation:
x = 38 - 13
x = 25
Therefore, the two numbers are 25 and 13.
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.
1) The sum of two numbers is 38: x + y = 38
2) Their difference is 12: x - y = 12
To solve this system of equations, we can use the method of substitution or addition/elimination.
Let's solve using the addition/elimination method:
Adding Equation 1 and Equation 2, we get:
(x + y) + (x - y) = 38 + 12
2x = 50
Dividing both sides by 2:
2x/2 = 50/2
x = 25
Now, substitute the value of x into one of the original equations (let's use Equation 1) to find y:
25 + y = 38
Subtracting 25 from both sides:
y = 38 - 25
y = 13
So, the two numbers are x = 25 and y = 13.