luke is thinking of two numbers whose sum is 14 and whose difference is 6. what numbers is luke thinking of?
The numbers are 10 and 4.
1 + 13
2 + 12
3 + 11
4 + 10
5 + 9
6 + 8
Which of those pairs of numbers has a difference of 6?
To find the two numbers Luke is thinking of, we can use a system of equations.
Let's assume the two numbers are x and y.
According to the information given, we know that the sum of the two numbers is 14:
Equation 1: x + y = 14
We also know that the difference between the two numbers is 6:
Equation 2: x - y = 6
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of elimination. We can eliminate one of the variables by adding the two equations together:
Adding Equation 1 and Equation 2:
(x + y) + (x - y) = 14 + 6
Simplifying:
2x = 20
Dividing both sides by 2:
x = 10
Now we can substitute the value of x into either of the original equations to find the value of y. Let's substitute it into Equation 1:
10 + y = 14
Subtracting 10 from both sides:
y = 4
Therefore, the two numbers Luke is thinking of are 10 and 4.