Question

the sum of two numbers is 18 and their difference is 4. find the numbers

Answer 1

Answer:

The sum means to add two numbers so we can write : x + y = 18

Then, their difference is 4 which can be written : x - y = 4

The best way to determine this is to set one of the variables on one side of an equation to use in the second equation. This takes a bit of algebra.

x + y = 18 can be rearranged to x = 18 - y OR y = 18 - x : either of these gives you an equation to plug in to the second equation to find one of the variables.

x - y = 4 , from the equation we rearranged before, y = 18-x so we can plug this equation in for y

x - (18-x) = 4

Now we only have x to solve for :

x-18 +x = 4 (the second x becomes a plus because of the negative on the outside of the parenthesis.

then if we add18 on both sides:

x +x = 4 +18

simplify : 2x = 22

x = 11

Then we plug 11 into the previous equations we started with:

x + y = 18 -----> 11 + y =18 -------> y = 7

x - y = 4 --------> does 11-7 = 4? Yes! So we found out that x = 11 and y = 7

Answer 2

Answer: 11, 7

Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 18. In other words, x plus y equals 18 and can be written as equation A:

x + y = 18

The difference between x and y is 4. In other words, x minus y equals 4 and can be written as equation B:

x - y = 4

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

x - y = 4

x = 4 + y

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

x + y = 18

4 + y + y = 18

4 + 2y = 18

2y = 14

y = 7

Now we know y is 7. Which means that we can substitute y for 7 in equation A and solve for x:

x + y = 18

x + 7 = 18

X = 11

Summary: The sum of two numbers is 18 and their difference is 4. What are the two numbers? Answer: 11 and 7 as proven here:

Sum: 11 + 7 = 18

Difference: 11 - 7 = 4