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

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) (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)

Start with the first equation.

Multiply both sides by 100 to clear out the decimals.

Distribute and multiply.

So the new first equation is

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

Move onto the second equation.

Multiply both sides by 100 to clear out the decimals.

Distribute and multiply.

So the new second equation is

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

So we have the system of equations:

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

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

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

Multiply and simplify

Combine like terms on the left side

Subtract 204660 from both sides

Combine like terms on the right side

Divide both sides by -1900 to isolate x

Divide

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

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms and reduce.

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

So the second part of our answer is:

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

So our answers are:

and

So this means that they made 7 forks and 20 spoons

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