Question

Amirah bought 7 books and 5 movies for a total of $71. Today, Amirah bought 23 books and 9 movies for a total of $159. Assuming neither item has changed in price, Find what is the cost of a book in dollars?

Answer 1

To find the cost of a book, we establish two equations based on Amirah's purchases and solve the system using the elimination method. After finding the cost of a movie, we can calculate the cost of a book.

Step-by-step explanation:

To determine the cost of a book, we can set up a system of linear equations using the information provided about Amirah's purchases. Let b represent the cost of a book and m represent the cost of a movie.

The cost of 7 books and 5 movies is $71, which can be written as the equation:

7b + 5m = 71

The cost of 23 books and 9 movies is $159, which gives us a second equation:
23b + 9m = 159

We can solve this system using the substitution or elimination method. For simplicity, we'll use the elimination method:

1. Multiply the first equation by -3 to eliminate the m variable:
   
   -3(7b + 5m) = -3(71)
   
   -21b - 15m = -213
2. Then, we add the resulting equation to the second equation:
   -21b - 15m + 23b + 9m = -213 + 159
   
   2b - 6m = -54
3. Isolate the variable b:
   2b = 6m - 54
4. Now divide both side by 2 to find b:
   b = (6m - 54)/2

Substitute the equation for b back into either of the original equations to find the value of m. After finding the cost of a movie, we can easily calculate the cost of a book.

Assuming without the loss of generality that the cost of a movie has not changed, we employ the first equation to solve for m and then use the value of m to determine b.