Question

The sum of 2 numbers is 30 and the difference is 10. What are the two numbers.

Answer 1

20 & 10 for obvious reasons they both make 30 and have a difference of 10

Answer 2

20 + 10 = 30

Explanation:

The sum of x and y is 30. In other words, x plus y equals 30 and can be written as equation A:

x + y = 30

The difference between x and y is 10. In other words, x minus y equals 10 and can be written as equation B:

x - y = 10

Now solve equation B for x to get the revised equation B:

x - y = 10

x = 10 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 30

10 + y + y = 30

10 + 2y = 30

2y = 20

y = 10

Now we know y is 10. Which means that we can substitute y for 10 in equation A and solve for x:

x + y = 30

x + 10 = 30

X = 20

Summary: The sum of two numbers is 30 and their difference is 10. What are the two numbers? Answer: 20 and 10 as proven here:

Sum: 20 + 10 = 30

Difference: 20 - 10 = 10