Question

At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $13.35. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks cost $19.50. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, what is the cost of each item?​

Answer 1

Answer: Pizza = $2.95, Breadstick = $0.50, Juice = $1.25

Step-by-step explanation:

Let P represent the cost of a slice of pizza

and B represent the cost of breadstick

and J represent the cost of a juice drink.

EQ1: 3P + 4B + 2J = 13.35

EQ2: 5P + 2B + 3J = 19.50

EQ3: 4B + J = P + 0.30     -->     P - 4B - J = -0.30

Let's eliminate B from EQ1 and EQ2 to form EQ4:

3P + 4B + 2J = 13.35   →  1(3P + 4B + 2J = 13.35)   →   3P + 4B + 2J =  13.35

5P + 2B + 3J = 19.50  → -2(5P + 2B + 3J = 19.50)  →  -10P -  4B -  6J = -39.00

                                                                        EQ4:     -7P          -4J    = -25.65

And eliminate B from EQ1 and EQ3 to form EQ5:

               3P + 4B + 2J = 13.35  

                 P -  4B  - J = -0.30

EQ5:       4P           + J  = 13.05    

Now, eliminate J from EQ4 and EQ5 to solve for P:

-7P  - 4J = -25.65  →    1(-7P  - 4J = -25.65)   →   -7P  - 4J = -25.65

 4P  +  J = 13.05   →    4(4P  +   J =  13.05)    →    16P  +4J =  52.20

                                                                             9P          = 26.55

                                                                           ÷9             ÷9    

                                                                                    P = 2.95

Plug in P = 2.95 into EQ4 or EQ5 to solve for J:

EQ5: 4P + J = 13.05

        4(2.95) + J = 13.05

        11.80 + J = 13.05

                   J = 1.25

Plug in P = 2.95 and J = 1.25 into either EQ1 or EQ2 or EQ3 to solve for B:

EQ3: 4B + J = P + 0.30

        4B + 1.25 = 2.95 + 0.30

        4B + 1.25 = 3.25

                   4B = 2.00

                     B = 0.50

Check (since we used EQ3 to find B, use either EQ1 or EQ2):

EQ2: 5P + 2B + 3J = 19.50

       5(2.95) + 2(0.50) + 3(1.25) = 19.50

       14.75 + 1.00 + 3.75 = 19.50

                            19.50 = 19.50     $\checkmark$