Word Problems (system of equations)
The sum of two numbers is 84. The larger exceeds the smaller by 22. What are the numbers?
Let's say the smaller of the two numbers is x. The larger of the two must be x + 22.
So, x + x + 22 = 2x + 22 = 84.
Subtract 22 from both sides to get 2x = 62.
Divided by 2 to get x = 31.
So the two numbers are 31 and 31 + 22 = 53.
We know two things. Our two numbers have a sum of 84 and one number is larger than the other by 22.
If we use x and y as variables, with x representing the smaller number and y representing the bigger number, we can find our answer.
If we substitute y for x+22, we can solve for x.
Now that we have x, we can solve for y.
Another way we could solve for y is by putting it back in the other equation.
OUr two numbers are 31 and 53.