Question

Adam and Barb planned a used book sale for the weekend so they gathered their books and agreed on a price for hardbacks and a lower price for paperbacks. Adam sold 14 hardcover books and 20 paperbacks and earned $234 for his efforts. Barb sold 15 hardcover books and 9 paperbacks. Barb made $201. How much did they charge for each hardcover book and for each paperback?
You must show your work.

1) Mathematically what kind of problem is this called? (What concept did you apply to this problem that allowed you to solve it?)


2) Set up the problem showing the equations you’ll use. Please make sure you label or explain what your variables mean.



3) Show the math work to arrive at the answer. Please make it clear which price is hardcover and which is paperback.

Answer 1

Answer:

Step-by-step explanation:

The text itself determined how to solve the problem.

Namely, two object are given in two relations and we conclude that we have two variables that we present with two equations.

We will take hardcover books as x and paperbacks as y.

First equation is  4x+10y=64

Second equation is  5x+7y=58

This is system of two linear equations with two variables

To solve this system we will use Gaussian agorithm with which we make

gradual elimination of the variables.

We will multiply first equation with number 4 and second with number (-5)

and get

20x+50y=320   and   -20x-28y=-232

When we add first equation to another we get

variable x is eliminated  

50y-28y=320-232 => 22y=88 => y=88/22=4

y=4  when we replace variable y in the first equation before multiplying

we get  4x+10*4=64 => 4x+40=64 => 4x=64-40 => 4x=24 => x=24/4=6

x=6

Total charge for hardcovers is  => 4x+5x=9x=9*6=54$

Total charge for paperbacks is => 10y+7y=17y=17*4=68$

Good luck!!!

Answer 2

Answer: hardcover books x=11 and paperbacks y=4

Step-by-step explanation:

14x+20y=234

15x+9y=201

Multiply the top equation by 9 and the bottom equation by 20 so the outcome of both equations would be 126x+180y=2106 and 300x+180y=4020 then you subtract the two equations once you do that you get 174x=1914, and the y variable cancels out, once you divide 174 from 1914 you get 11x. So the answer for how much hardcover books cost is 11 dollars. Now we have to find the y variable which we can just plug in 11 (x) into the equation. So 15(11)+9y=201 we get 165+9y=201, subtract 165 from both sides and we get 9y=36 and divide 9 from both sides and we get 4 so y=4 the cost of paperbacks are 4 dollars