or

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Mario's Pizza just received two big orders from customers throwing parties. The first customer, Kendall, bought 8 regular pizzas and 8 deluxe pizzas and paid $232. The second customer, Eric, ordered 8 regular pizzas and 7 deluxe pizzas, paying a total of $213. What is the price of each pizza?

Each regular pizza costs $
, and each deluxe pizza costs $
.

Answer 1

Let the cost of each regular pizza be $r and the cost of each deluxe pizza be $d.

The given information can be translated into the following system of equations:

8r + 8d = 232 (Equation 1) (for Kendall's order)
8r + 7d = 213 (Equation 2) (for Eric's order)

To solve this system of equations, we can use the method of substitution or elimination.

Using the method of elimination, we can multiply Equation 2 by 8 to match the coefficients of r in both equations:

64r + 56d = 1704 (Equation 3)

Next, we can subtract Equation 1 from Equation 3 to eliminate the variables r:

(64r + 56d) - (8r + 8d) = 1704 - 232
56r + 48d = 1472 (Equation 4)

Now, we have a new equation with only one variable (d). We can solve it to find the value of d.

Subtract Equation 4 from Equation 1 to eliminate the variables r:

(8r + 8d) - (56r + 48d) = 232 - 1472
-48r - 40d = -1240

We can multiply this equation by -1 to simplify it:

48r + 40d = 1240 (Equation 5)

Now, we can add Equation 4 and Equation 5 to eliminate the variable r:

(56r + 48d) + (48r + 40d) = 1472 + 1240
104r + 88d = 2712

Dividing both sides of this equation by 8, we get:

13r + 11d = 339 (Equation 6)

Now, we have a new equation with only one variable (d). We can solve it to find the value of d.

Multiplying Equation 6 by 5 to simplify it:

65r + 55d = 1695 (Equation 7)

Now, we can subtract Equation 5 from Equation 7 to eliminate the variable r:

(65r + 55d) - (48r + 40d) = 1695 - 1240
17r + 15d = 455

Next, we can multiply Equation 2 by 15 to simplify it:

120r + 105d = 3195

Now, we can subtract Equation 7 from Equation 8 to eliminate the variable r:

(120r + 105d) - (17r + 15d) = 3195 - 455
103r + 90d = 2740

We can divide this equation by 5:

20r + 18d = 548

Now, we have a new equation with only one variable (r). We can solve it to find the value of r.

Subtract Equation 7 from Equation 9 to eliminate the variable d:

(20r + 18d) - (65r + 55d) = 548 - 1695
-45r - 37d = -1147

Now we can multiply equation by -8:

360r + 296d = 9184

Now subtract Equation 9 from Equation 10 to eliminate the variable r:

(360r + 296d) - (17r + 15d) = 9184 - 2740
343r + 281d = 6444

Dividing each side by 77 we find that

r+3.25d = 18.54

Now subtract 2*r+6.5d = 37.18 from Equation 11

-343r-89d = -14618

Solving this equation we find that

d = ???
r = ???