Question

One number is seven less than another. Their sum is thirteen. Find the numbers.

Answer 1

The numbers are 10 and 3.

Step-by-step explanation:

1. Set up equations relating the two numbers to each other.
2. Solve for the two variables.

STEP 1: Based on the problem, two equations can be set up:

First, "one number is seven less than another." This can be expressed mathematically:

Let x = first number

      y = second number

$x \ - 7 = \ y$

The second equation is based on "their sum is thirteen."

$x \ + \ y \ = 13$

STEP 2: Solve for the variables.

In this step, substitute the value of y from Equation 1 into Equation 2:

$x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13$

Next, solve for x by manipulating the equation:

$2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}$

Now that the value of x is known, it can be used to determine the value of y.

To do this, use the calculated value for x and plug it into Equation 1:

$y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}$

Learn More

1. Learn more about system equations brainly.com/question/3056782
2. Learn more about transposition brainly.com/question/260793
3. Learn more about word problems brainly.com/question/11052962

Keywords: two equations, two variables