Question

First, complete the story below so that it can be represented by the equation 22x = 14 + 20x.
Then, solve for x.
(a) Dante is going to buy x pizzas tonight.
Restaurant A charges Sl per pizza, with no other charges or discounts.
Restaurant B charges $ per pizza, and there is a $____(delivery charge, coupon discount) • The total cost (with all charges and discounts) is ( more for restaurants a, ire for restaurants b, same for both)
(b) For this equation (and story): x=___

Answer 1

### Completed Story

Dante is going to buy \( x \) pizzas tonight. Restaurant A charges $11 per pizza, with no other charges or discounts. Restaurant B charges $10 per pizza, and there is a $14 delivery charge. The total cost (with all charges and discounts) is more for Restaurant A.

### Set Up the Equation

Now, let's set up the equation according to the costs:

- The total cost for Restaurant A is:
\[
11x
\]

- The total cost for Restaurant B is:
\[
10x + 14
\]

According to the story, Restaurant A costs more than Restaurant B, so we can set the equation as follows:
\[
11x = 10x + 14
\]

To simplify, we can subtract \( 10x \) from both sides:
\[
11x - 10x = 14
\]

This leads us to:
\[
x = 14
\]

### Answer

(a) Restaurant A charges $11 per pizza, and there is a $14 delivery charge for Restaurant B. The total cost is more for Restaurant A.

(b) For this equation (and story): \( x = 14 \)