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The sum of two numbers is 84. The larger exceeds the smaller by 22. What are the numbers?

Word Problems (system of equations)

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2 Answers

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.

x+y=84

y=x+22

If we substitute y for x+22, we can solve for x.

x+x+22=84

2x+22=84

2x=62

x=31

Now that we have x, we can solve for y.

y=x+22 

y=31+22

y=53.

Another way we could solve for y is by putting it back in the other equation.

x+y=84

31+y=84

y=53

OUr two numbers are 31 and 53.