One number is seven less than another. Their sum is thirteen. Find the numbers.(smaller value)(larger value) isn't there more than 1 possible combination here? how do i know which one it wants?
Accepted Solution
A:
The numbers are 10 and 3.Step-by-step explanation:Set up equations relating the two numbers to each other.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[tex]x \ - 7 = \ y[/tex]The second equation is based on "their sum is thirteen."[tex]x \ + \ y \ = 13[/tex]STEP 2: Solve for the variables.In this step, substitute the value of y from Equation 1 into Equation 2:[tex]x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13\\[/tex]Next, solve for x by manipulating the equation:[tex]2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}[/tex]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:[tex]y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}[/tex]Learn MoreLearn more about system equations more about transposition more about word problems : two equations, two variables