Question

(a) complete the story below so that it can be represented by the equation 14x = 16x - 12. bill is going to buy x copies of a book. store a charges $\square$ per copy, with no other charges or discounts. store b charges $\square$ per copy, and there is a $\square$ select the total cost (with all charges and discounts) is select (b) solve for x. for this equation (and story): x = $\square$

Explanation:

Part (a)

To form the story for the equation \(14x = 16x - 12\):

• For Store A: The cost is \(14x\), so Store A charges \(\$14\) per copy (since cost = price per copy \(\times\) number of copies, \(x\)).
• For Store B: The cost is \(16x - 12\). This means Store B charges \(\$16\) per copy (the \(16x\) term) and there is a \(\$12\) discount (because we subtract 12, so it's a discount or reduction in total cost). The total cost (with all charges and discounts) is such that Store A's total cost equals Store B's total cost (since the equation is \(14x = 16x - 12\), meaning the total cost from both stores is equal for \(x\) copies).

So filling in the blanks:

• Store A charges \(\boldsymbol{\$14}\) per copy.
• Store B charges \(\boldsymbol{\$16}\) per copy, and there is a \(\boldsymbol{\$12}\) discount.
• The total cost (with all charges and discounts) is equal for both stores (so the relationship is that the total cost from Store A equals the total cost from Store B).

Part (b)

Step 1: Start with the equation

We have the equation \(14x = 16x - 12\). Our goal is to solve for \(x\). First, we want to get all the \(x\)-terms on one side. Subtract \(16x\) from both sides.

$$ 14x - 16x = 16x - 12 - 16x $$

Step 2: Simplify both sides

Simplifying the left side: \(14x - 16x = -2x\). Simplifying the right side: \(16x - 16x - 12 = -12\). So now we have:

$$ -2x = -12 $$

Step 3: Solve for \(x\)

Divide both sides by \(-2\) to isolate \(x\).

$$ \frac{-2x}{-2} = \frac{-12}{-2} $$

Step 4: Simplify the fractions

Simplifying both sides, we get:

$$ x = 6 $$

Answer:

(Part b):
For this equation (and story): \(x = \boldsymbol{6}\)