Question

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A bookstore sold 525 copies of dictionaries and 705 copies of cookbooks. A total of $7500 was spent on the purchase. Write an equation in Standard Form to model the problem where dictionaries are (x) and cookbooks are (y). Then answer the question that follows.
A) Standard Form equation:
B) If dictionaries sold for $10 each, what price did the cookbooks sell for? (Round to the penny)
Cookbooks = $

Answer 1

The standard form equation for a bookstore selling 525 dictionaries (x) and 705 cookbooks (y) at $10 each is 10x + 3.19y = 7500. Cookbooks sold for approximately $3.19 each.

A) Standard Form Equation:

Let x represent the number of dictionaries and y represent the number of cookbooks.

The total number of books sold is the sum of dictionaries and cookbooks: x + y = 525 + 705.

The total cost spent on the purchase is $7500, and the cost per dictionary is $10, and the cost per cookbook is c. Therefore, the equation is
`\( 10x + c \cdot y = 7500 \)`.

So, the standard form equation is:

`\[ x + y = 525 + 705 \]\[ 10x + c \cdot y = 7500 \]`

B) If dictionaries sold for $10 each, the equation becomes:

`\[ 10x + c \cdot y = 7500 \]`

Since dictionaries sold for $10 each, c is the price of cookbooks. Solve for c:

`\[ c \cdot y = 7500 - 10x \]\[ c = (7500 - 10x)/(y) \]`

Now, substitute the given values (525 dictionaries and 705 cookbooks) to find \( c \):

`\[ c = (7500 - 10 \cdot 525)/(705) \]\[ c \approx (7500 - 5250)/(705) \]\[ c \approx (2250)/(705) \]\[ c \approx 3.19 \]`

Therefore, the cookbooks sold for approximately $3.19 each (rounded to the penny).