The sum of two numbers is equal to 63 and their difference is equal to 12. Find the numbers.
x + y = 63
x - y = 12
x = 63 - y
63 - y - y = 12
-2y = - 51
y = 25.5
x + 25.5 = 63
x = 37.5
Well, these two numbers seem to be having quite the circus act going on! Let's call our first number "X" and our second number "Y". According to the wacky information given, we know that X + Y = 63 and X - Y = 12.
Now, buckle up for some math magic! Let's solve this puzzling situation. Let's add the equations together like we're juggling numbers: (X + Y) + (X - Y) = 63 + 12.
When we simplify that equation, we get 2X = 75. Now, it's time to divide both sides by 2, just to make sure things stay balanced, and we get X = 37.5.
Hmm, wait a minute! We have a decimal in our result! That's no fun at all for our circus act. Let's try a different trick. Let's rewrite our second equation: X - Y = 12. We can rearrange this equation to get X = Y + 12.
Now we'll substitute X in our first equation (X + Y = 63) with Y + 12: (Y + 12) + Y = 63.
When we simplify this equation, we get 2Y + 12 = 63. Let's subtract 12 from both sides to keep things balanced, and we get 2Y = 51. After dividing both sides by 2, Y = 25.5.
Uh-oh! Another decimal! Our circus act just got even crazier! It looks like these numbers are playing tricks on us. Let's try a different approach, shall we?
Given that the sum of these two numbers is 63, let's say our first number, X, is some unknown value. The second number, Y, would then be 63 - X.
Now, according to our second piece of wacky information, X - Y = 12. We can substitute Y with 63 - X in this equation: X - (63 - X) = 12.
When we solve this equation, we find that X = 37.5 and Y = 25.5.
So, it seems these pesky numbers are insisting on being decimals. Maybe they're just clowning around, after all!
Let's assign variables to represent the two numbers. Let's call the first number "x" and the second number "y".
According to the problem, the sum of the two numbers is equal to 63. We can write this as an equation:
x + y = 63 -- Equation 1
The problem also states that the difference between the two numbers is equal to 12. We can write this as another equation:
x - y = 12 -- Equation 2
To find the values of x and y, we need to solve this system of equations.
We can use the method of substitution to solve the system. First, we solve for one variable in terms of the other in one of the equations. Let's solve Equation 2 for x:
x = y + 12
Now we substitute this expression for x into Equation 1:
(y + 12) + y = 63
Simplifying, we combine like terms:
2y + 12 = 63
Next, we isolate the variable y by subtracting 12 from both sides:
2y = 63 - 12
2y = 51
Finally, we solve for y by dividing both sides by 2:
y = 51 / 2
y = 25.5
Now that we have the value of y, we can substitute it back into Equation 2 to find x:
x - 25.5 = 12
Adding 25.5 to both sides:
x = 12 + 25.5
x = 37.5
So the two numbers are x = 37.5 and y = 25.5.
To find the numbers, let's assign variables to represent the unknown numbers. Let's call the first number "x" and the second number "y."
Based on the given information, we have two equations:
Equation 1: x + y = 63
Equation 2: x - y = 12
To solve this system of equations, we will use the method of substitution.
From Equation 2, we can isolate x by adding y to both sides:
x = y + 12
Now we can substitute this expression for x into Equation 1:
(y + 12) + y = 63
Simplifying this equation:
2y + 12 = 63
2y = 63 - 12
2y = 51
Finally, divide both sides of the equation by 2 to solve for y:
y = 51 / 2
y = 25.5
Now, substitute the value of y back into Equation 2 to find x:
x - 25.5 = 12
x = 12 + 25.5
x = 37.5
Therefore, the two numbers are 37.5 and 25.5.