Math Problem Statement

The sum of two numbers is 90. The difference is 12. What are the numbers?

Solution

The problem states:

  • The sum of two numbers is 90.
  • Their difference is 12.
  • We are asked to find the two numbers.

Let the two numbers be represented by xx and yy.

We have the following system of equations:

  1. x+y=90x + y = 90 (the sum of the two numbers)
  2. xy=12x - y = 12 (the difference of the two numbers)

Now, we can solve this system of equations using the addition method. By adding both equations:

(x+y)+(xy)=90+12(x + y) + (x - y) = 90 + 12

Simplifying:

2x=1022x = 102

Solving for xx:

x=1022=51x = \frac{102}{2} = 51

Now substitute x=51x = 51 into the first equation x+y=90x + y = 90:

51+y=9051 + y = 90

Solving for yy:

y=9051=39y = 90 - 51 = 39

Thus, the two numbers are 5151 and 3939.

Would you like further details on how I solved this? Or do you have another question?

Here are some related questions you can explore:

  1. How do you solve systems of linear equations by substitution?
  2. What are some real-world applications of systems of equations?
  3. How do you graph the solutions to a system of linear equations?
  4. How can we solve a system of equations if one equation involves multiplication?
  5. How do you check the solution to a system of equations?

Tip: When solving systems of equations, always check your solutions by substituting them back into the original equations to verify they satisfy both equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations

Formulas

x + y = 90
x - y = 12

Theorems

Addition and Substitution Methods

Suitable Grade Level

Grades 6-8