The difference of two numbers is 3. Their sum is 13. Find the numbers.
a - b = 3
a + b = 13
How do I solve it?
Think about the numbers that add up to 13,
6 + 7
5 + 8
4 + 9
3 + 10
Which pair when one is subtracted from the other gives us 3 for an answer?
To solve this problem, we can use a system of equations. Let's call the two numbers x and y.
1. The difference of two numbers is 3:
This can be expressed as: x - y = 3.
2. Their sum is 13:
This can be expressed as: x + y = 13.
Now, we have a system of two equations with two unknowns. We can solve it by using elimination, substitution, or any other method.
Let's use the substitution method:
1. Solve one equation for one variable. Let's solve the first equation for x:
x = y + 3.
2. Substitute the value of x in the second equation:
(y + 3) + y = 13.
3. Simplify and solve for y:
2y + 3 = 13
2y = 10
y = 5.
4. Now, substitute the value of y back into either of the original equations. Let's use the first equation:
x - 5 = 3
x = 3 + 5
x = 8.
So, the two numbers are 8 and 5.