john thinks of 2 different numbers .they have a sum of 12 and a difference of 2 .what are tow numbers?
even with no algebra, just think of the ways you can add up to 12. Which way has the numbers 2 apart?
5+7 = 12
Now, if you want to exercise your algebra,
x+y=12
x-y=2
Solve that for x and y
To find the two numbers, we can set up a system of equations. Let's call the two numbers x and y.
From the given information, we have two equations:
1. x + y = 12 (sum of the numbers is 12)
2. x - y = 2 (difference of the numbers is 2)
We can solve this system of equations using the method of substitution or elimination.
Method 1: Substitution
Solve one equation for one variable and substitute it into the other equation.
From equation 2, we can solve for x:
x = y + 2
Substitute this value of x into equation 1:
(y + 2) + y = 12
2y + 2 = 12
2y = 12 - 2
2y = 10
y = 10 / 2
y = 5
Now substitute the value of y back into equation 2 to find x:
x - 5 = 2
x = 2 + 5
x = 7
Therefore, the two numbers are 7 and 5.
Method 2: Elimination
Add equations 1 and 2 to eliminate one variable:
(x + y) + (x - y) = 12 + 2
2x = 14
x = 14 / 2
x = 7
Substitute the value of x into equation 1 to find y:
7 + y = 12
y = 12 - 7
y = 5
Again, the two numbers are 7 and 5.
So, the two numbers John is thinking of are 7 and 5.