SOLUTION: Hi, I need help with this problem, I have tried everything. Here it is: The difference of two numbers is 33. If four times the lesser number is subtracted from three times the g

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi, I need help with this problem, I have tried everything. Here it is: The difference of two numbers is 33. If four times the lesser number is subtracted from three times the g      Log On


   

Question 164534: Hi, I need help with this problem, I have tried everything. Here it is: The difference of two numbers is 33. If four times the lesser number is subtracted from three times the greater number, the difference is 62. Find the number.
The directions say to choose a variable & use it with the given facts. Then write an open sentence that represents the relationship among the numbers in the problem. Finally, solve the open sentence and find the required numbers.
Thank you so much for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The difference of two numbers is 33" translates to x-y=33 and the statement "four times the lesser number is subtracted from three times the greater number, the difference is 62" is the equation 3x-4y=62





So we have the system of equations:

system%28x-y=33%2C3x-4y=62%29


Let's solve the system by use of substitution.


In order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x-y=33 Start with the first equation


-y=33-x Subtract x from both sides


-y=-x%2B33 Rearrange the equation


y=%28-x%2B33%29%2F%28-1%29 Divide both sides by -1


y=%28%28-1%29%2F%28-1%29%29x%2B%2833%29%2F%28-1%29 Break up the fraction


y=x-33 Reduce



---------------------

Since y=x-33, we can now replace each y in the second equation with x-33 to solve for x



3x-4highlight%28%28x-33%29%29=62 Plug in y=x-33 into the second equation. In other words, replace each y with x-33. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B%28-4%29%281%29x%2B%28-4%29%28-33%29=62 Distribute -4 to x-33


3x-4x%2B132=62 Multiply


-x%2B132=62 Combine like terms on the left side


-x=62-132Subtract 132 from both sides


-x=-70 Combine like terms on the right side


x=%28-70%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=70 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=70









Since we know that x=70 we can plug it into the equation y=x-33 (remember we previously solved for y in the first equation).



y=x-33 Start with the equation where y was previously isolated.


y=%2870%29-33 Plug in x=70


y=70-33 Multiply


y=37 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=37









-----------------Summary------------------------------

So the answers are:


x=70 and y=37


This means that the two numbers are 70 and 37