SOLUTION: The difference of two positive numbers is 8 . The larger number is twenty-one less than twice the smaller number. Find the numbers.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The difference of two positive numbers is 8 . The larger number is twenty-one less than twice the smaller number. Find the numbers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1123787: The difference of two positive numbers is
8
. The larger number is twenty-one less than twice the smaller number. Find the numbers.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's the larger number be x and the smaller number y
if the difference of two positive numbers is 8, we have
x-y=8...eq.1
if the larger number is twenty-one less than twice the smaller number, we have
x%2B21=2y........eq.2

to find the numbers, solve this system:
x-y=8...eq.1
x%2B21=2y........eq.2
----------------------------substitute eq.2 from eq.1
x-y-%28x%2B21%29=8-2y
x-y-x-21=8-2y
-y-21=8-2y
2y-y=8%2B21
y=29
substitute in eq.2, and solve for x
x%2B21=2y........eq.2
x%2B21=2%2A29
x=58-21
x=37
so, the larger number is 37 and the smaller number is 29