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

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
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