SOLUTION: It costs $1.70 to buy supplies to make a fork and $1.30 to buy supplies to make a spoon. The store sells the fork for $5.60 and the spoon for $5.40. They spent $37.90 on materials

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: It costs $1.70 to buy supplies to make a fork and $1.30 to buy supplies to make a spoon. The store sells the fork for $5.60 and the spoon for $5.40. They spent $37.90 on materials       Log On


   

Question 182960: It costs $1.70 to buy supplies to make a fork and $1.30 to buy supplies to make a spoon. The store sells the fork for $5.60 and the spoon for $5.40. They spent $37.90 on materials for forks and spoons. They sold the finished product for $147.20. How many forks and how many spoons did they make?
I did 1.70x + 1.30y = 37.90 as one of my equations
5.60x + 5.40y = 147.20 for my other
I have tried substitution and get tangled up with the decimals
I have tried addition and get messed up. Seems I get decimal answers and can't seem to work it into a whole fork or whole spoon without it being a decimal. What am I doing wrong, or are my equations not correct and this is where Im going wrong.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can solve this system with the decimal values, but I always find it easier to get rid of the decimal numbers. To do this, simply multiply both sides of the equations by 100 (which will move EVERY decimal place 2 spots to the right)


1.70x+%2B+1.30y+=+37.90 Start with the first equation.


100%281.70x%2B1.30y%29=100%2837.90%29 Multiply both sides by 100 to clear out the decimals.


170x%2B130y=3790 Distribute and multiply.


So the new first equation is 170x%2B130y=3790

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


5.60x+%2B+5.40y+=+147.20 Move onto the second equation.


100%285.60x%2B5.40y%29=100%28147.20%29 Multiply both sides by 100 to clear out the decimals.


560x%2B540y=14720 Distribute and multiply.


So the new second equation is 560x%2B540y=14720

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


So we have the system of equations:


system%28170x%2B130y=3790%2C560x%2B540y=14720%29


Let's use substitution to solve this system.


Now 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

170x%2B130y=3790 Start with the first equation


130y=3790-170x Subtract 170x from both sides


130y=-170x%2B3790 Rearrange the equation


y=%28-170x%2B3790%29%2F%28130%29 Divide both sides by 130


y=%28%28-170%29%2F%28130%29%29x%2B%283790%29%2F%28130%29 Break up the fraction


y=%28-17%2F13%29x%2B379%2F13 Reduce



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

Since y=%28-17%2F13%29x%2B379%2F13, we can now replace each y in the second equation with %28-17%2F13%29x%2B379%2F13 to solve for x



560x%2B540highlight%28%28%28-17%2F13%29x%2B379%2F13%29%29=14720 Plug in y=%28-17%2F13%29x%2B379%2F13 into the second equation. In other words, replace each y with %28-17%2F13%29x%2B379%2F13. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



560x%2B%28540%29%28-17%2F13%29x%2B%28540%29%28379%2F13%29=14720 Distribute 540 to %28-17%2F13%29x%2B379%2F13


560x-%289180%2F13%29x%2B204660%2F13=14720 Multiply


Multiply EVERY term by the LCD 13. This will eliminate the fractions



7280x-9180x%2B204660=191360 Multiply and simplify



-1900x%2B204660=191360 Combine like terms on the left side


-1900x=191360-204660 Subtract 204660 from both sides


-1900x=-13300 Combine like terms on the right side


x=%28-13300%29%2F%28-1900%29 Divide both sides by -1900 to isolate x



x=7 Divide





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


So the first part of our answer is: x=7









Since we know that x=7 we can plug it into the equation y=%28-17%2F13%29x%2B379%2F13 (remember we previously solved for y in the first equation).



y=%28-17%2F13%29x%2B379%2F13 Start with the equation where y was previously isolated.


y=%28-17%2F13%29%287%29%2B379%2F13 Plug in x=7


y=-119%2F13%2B379%2F13 Multiply


y=20 Combine like terms and reduce.


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


So the second part of our answer is: y=20









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

So our answers are:

x=7 and y=20


So this means that they made 7 forks and 20 spoons