Question

(a) complete the story below so that it can be represented by the equation 22x = 18x + 12. amanda is going to buy x pizzas tonight. restaurant a charges $\square$ per pizza, with no other charges or discounts. restaurant b charges $\square$ per pizza, 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)

Step1: Analyze the equation structure

The equation is \(22x = 18x + 12\). In a cost - per - pizza context, the left - hand side \(22x\) represents the total cost from Restaurant A, where \(22\) is the cost per pizza and \(x\) is the number of pizzas. The right - hand side \(18x+12\) represents the total cost from Restaurant B, where \(18\) is the cost per pizza and \(12\) is a fixed additional charge (like a delivery fee or a base charge).
So, Restaurant A charges \(\$22\) per pizza. Restaurant B charges \(\$18\) per pizza, and there is a \(\$12\) fixed charge (for example, a delivery fee). The total cost (with all charges and discounts) is equal for both restaurants (since the equation is set as \(22x=18x + 12\), meaning the total cost from A equals the total cost from B).

Part (b)

Step1: Solve the equation \(22x=18x + 12\) for \(x\)

Subtract \(18x\) from both sides of the equation.
\(22x-18x=18x + 12-18x\)
Simplify both sides: \(4x=12\)

Step2: Isolate \(x\)

Divide both sides of the equation \(4x = 12\) by \(4\).
\(\frac{4x}{4}=\frac{12}{4}\)
We get \(x = 3\)

Answer:

(a) Restaurant A charges \(\boldsymbol{22}\) per pizza, Restaurant B charges \(\boldsymbol{18}\) per pizza, and there is a \(\boldsymbol{12}\) fixed charge. The total cost (with all charges and discounts) is equal for both restaurants.
(b) \(\boldsymbol{x = 3}\)