The sum of two numbers is 12. The difference of the same two numbers is 24. What is the larger of the two numbers?
12 and 6
Let's assume the two numbers are x and y.
According to the problem, we have the following equations:
1. x + y = 12 (the sum of the two numbers is 12)
2. x - y = 24 (the difference of the two numbers is 24)
To solve for the larger number, we need to eliminate one of the variables.
By adding equation 1 and equation 2, we can eliminate y:
(x + y) + (x - y) = 12 + 24
x + y + x - y = 36
2x = 36
Dividing both sides of the equation by 2, we get:
x = 18
Now, substituting the value of x into either equation 1 or 2, we can solve for y:
x + y = 12
18 + y = 12
y = 12 - 18
y = -6
Therefore, the larger of the two numbers is 18.
To find the larger of the two numbers, let's solve this problem step by step:
1. Let's assume the two numbers are x and y, where x is the larger number.
2. We are given two pieces of information:
- The sum of the two numbers is 12, which can be mathematically written as x + y = 12.
- The difference between the two numbers is 24, which can be written as x - y = 24.
3. Now we have a system of two equations with two variables:
- x + y = 12
- x - y = 24
4. To solve this system of equations, we can use the method of substitution or elimination.
- Let's use the method of elimination:
- Adding the two equations together eliminates the y term:
(x + y) + (x - y) = 12 + 24
2x = 36
- Dividing both sides of the equation by 2, we get:
x = 18
5. Now that we've found the value of x, the larger number is 18.
Therefore, the larger of the two numbers is 18.
x+y = 12
x-y = 24
2x = 36
x = 18
y = -6
I figure you can pick the larger one.