Question 13174: The Regal Book Store has 100 overstocked books to sell. The manager is going to mark some of the books $2 each and the remaining books $3 each. How many books must be priced at each price to recieve $245?
Found 2 solutions by akmb1215, kunal_122:
Answer by akmb1215(68)   (Show Source):
You can put this solution on YOUR website! You should set up a system of equations to solve this problem. You know that some books are marked $2, and some are marked $3. You should assign variables to each kind of book...I am going to use C (for cheap - the $2 ones) and E (for expensive - the $3 ones).
For the first equation, add the number of books together, and you get 100 (because that is how many books the problem tells you they have to sell). So, the first equation is  , because if you add all the cheap books and all the expensive books together, you will get 100 total books.
For the second equation, you need to add the prices together. Each cheap book, C, costs $2...and each expensive book, E, costs $3. Added together, you know the prices will be $245 (because that is what the problem tells you). So, the second equation is  .
To solve the system of equations by substitution, you need to solve the first equation for the variable C. To do this, move the E to the other side by subtracting it from both sides of the equation. You end up with  . Now you can plug 100-E in for C in the second equation. When you do this, you will get  . To solve this equation, first use the distributive property to get  . Now, combine like terms to get  . Move 200 to the right side of the equal sign by subtracting it from both sides of the equation. You end up with  . This means that there were 45 expensive books.
Now, you can plug 45 into the first original equation to solve for C.  . Solve by subtracting 45 from both sides, and you get C = 55.
They will need to price 45 books at $3 each..and 55 books at $2 each.
Answer by kunal_122(19) (Show Source):
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