SOLUTION: Find the two numbers whose sum is 45 and such that one is 4 times as large as the other.

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Find the two numbers whose sum is 45 and such that one is 4 times as large as the other.      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 132922: Find the two numbers whose sum is 45 and such that one is 4 times as large as the other.
Answer by jim_thompson5910(14873) About Me  (Show Source):
You can put this solution on YOUR website!
"two numbers whose sum is 45"---> x%2By=45

"one is 4 times as large"----> y=4x



Start with the given system
x%2By=45
y=4x



x%2B4x=45 Plug in y=4x into the first equation. In other words, replace each y with 4x. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



5x=45 Combine like terms on the left side


x=%2845%29%2F%285%29 Divide both sides by 5 to isolate x



x=9 Divide. So our first number is 9




Now that we know that x=9, we can plug this into y=4x to find y



y=4%289%29 Substitute 9 for each x


y=36 Simplify. So our second number is 36


So our answer is x=9 and y=36 which means that our two numbers are 9 and 36