Math / Algebra

QuestionYour local pizza store sells medium pizzas for $\$ 7.69$ each, and breadsticks for $\$ 3.49$ per order. For a party, you decide to order 5 pizzas and 3 orders of breadsticks. There is a $\$ 3$ delivery fee, and a $9.4 \%$ sales tax will be added to the total, including the delivery fee. What will be the total bill after tax, rounded to the nearest cent? $\$$ $\square$ Suppose you have a budget of $\$ 143.97$ to spend, and you order 14 pizzas. How many orders of breadsticks can you get, assuming the same delivery fee and sales tax? Round your answer to the nearest whole number. $\qquad$ orders of breadsticks
Suppose you have a budget of $\$ 306.79$ to spend, and you order 20 orders of breadsticks. How many pizzas can you get, assuming the same delivery fee and sales tax? Round your answer to the nearest whole number. $\square$ pizzas Question Help: Message instructor Post to forum Submit Question

Studdy Solution

STEP 1

1. Medium pizzas cost $7.69 each<br />2. Breadsticks cost$ 3.49 per order
3. There is a $3 delivery fee
4. Sales tax is 9.4% and applies to the total including the delivery fee
5. All calculations should be rounded to the nearest cent unless otherwise specified

STEP 2

1. Calculate the cost of pizzas and breadsticks
2. Add the delivery fee
3. Calculate and add the sales tax
4. Solve for the number of breadstick orders with a fixed budget and pizza order
5. Solve for the number of pizzas with a fixed budget and breadstick order

STEP 3

Calculate the cost of pizzas and breadsticks: Cost of pizzas: $5 \times \$7.69 = \$38.45$ Cost of breadsticks: $3 \times \$3.49 = \$10.47$ Subtotal: $\$38.45 + \$10.47 = \$48.92$

STEP 4

Add the delivery fee: $\$48.92 + \$3.00 = \$51.92$

STEP 5

Calculate and add the sales tax: Tax amount: $\$51.92 \times 0.094 = \$4.88048$ Total bill after tax: $\$51.92 + \$4.88048 = \$56.80048$ Rounded to the nearest cent: $\$56.80$
The total bill after tax is $\$56.80$ .

STEP 6

To solve for the number of breadstick orders with a budget of $143.97 and 14 pizzas:
Cost of 14 pizzas: $14 \times \$7.69 = \$107.66$ Remaining budget for breadsticks and fees: $\$143.97 - \$107.66 = \$36.31$
Let x be the number of breadstick orders. We can set up the equation: $(14 \times 7.69) + (x \times 3.49) + 3 + [(14 \times 7.69) + (x \times 3.49) + 3] \times 0.094 = 143.97$
Simplifying: $107.66 + 3.49x + 3 + (107.66 + 3.49x + 3) \times 0.094 = 143.97$ $110.66 + 3.49x + 10.40204 + 0.32806x = 143.97$ $121.06204 + 3.81806x = 143.97$ $3.81806x = 22.90796$ $x = 6.00$
Rounding to the nearest whole number: 6 orders of breadsticks

STEP 7

To solve for the number of pizzas with a budget of $306.79 and 20 orders of breadsticks:
Cost of 20 orders of breadsticks: $20 \times \$3.49 = \$69.80$ Remaining budget for pizzas and fees: $\$306.79 - \$69.80 = \$236.99$
Let y be the number of pizzas. We can set up the equation: $(y \times 7.69) + (20 \times 3.49) + 3 + [(y \times 7.69) + (20 \times 3.49) + 3] \times 0.094 = 306.79$
Simplifying: $7.69y + 69.80 + 3 + (7.69y + 69.80 + 3) \times 0.094 = 306.79$ $7.69y + 72.80 + 0.72286y + 6.8412 = 306.79$ $8.41286y + 79.6412 = 306.79$ $8.41286y = 227.1488$ $y = 27.00$
Rounding to the nearest whole number: 27 pizzas

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Studdy Solution

STEP 1

1. Medium pizzas cost $7.69 each<br />2. Breadsticks cost$ 3.49 per order
3. There is a $3 delivery fee
4. Sales tax is 9.4% and applies to the total including the delivery fee
5. All calculations should be rounded to the nearest cent unless otherwise specified

STEP 2

1. Calculate the cost of pizzas and breadsticks
2. Add the delivery fee
3. Calculate and add the sales tax
4. Solve for the number of breadstick orders with a fixed budget and pizza order
5. Solve for the number of pizzas with a fixed budget and breadstick order

STEP 3

Calculate the cost of pizzas and breadsticks: Cost of pizzas: $5 \times \$7.69 = \$38.45$ Cost of breadsticks: $3 \times \$3.49 = \$10.47$ Subtotal: $\$38.45 + \$10.47 = \$48.92$

STEP 4

Add the delivery fee: $\$48.92 + \$3.00 = \$51.92$

STEP 5

Calculate and add the sales tax: Tax amount: $\$51.92 \times 0.094 = \$4.88048$ Total bill after tax: $\$51.92 + \$4.88048 = \$56.80048$ Rounded to the nearest cent: $\$56.80$
The total bill after tax is $\$56.80$ .

STEP 6

STEP 7

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Studdy Solution

STEP 1

STEP 2

1. Calculate the cost of pizzas and breadsticks2. Add the delivery fee3. Calculate and add the sales tax4. Solve for the number of breadstick orders with a fixed budget and pizza order5. Solve for the number of pizzas with a fixed budget and breadstick order

STEP 3

Calculate the cost of pizzas and breadsticks: Cost of pizzas: 5×$7.69=$38.455 \times \$7.69 = \$38.455×$7.69=$38.45 Cost of breadsticks: 3×$3.49=$10.473 \times \$3.49 = \$10.473×$3.49=$10.47 Subtotal: $38.45+$10.47=$48.92\$38.45 + \$10.47 = \$48.92$38.45+$10.47=$48.92

STEP 4

Add the delivery fee: $48.92+$3.00=$51.92\$48.92 + \$3.00 = \$51.92$48.92+$3.00=$51.92

STEP 5

STEP 6

STEP 7

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1. Calculate the cost of pizzas and breadsticks
2. Add the delivery fee
3. Calculate and add the sales tax
4. Solve for the number of breadstick orders with a fixed budget and pizza order
5. Solve for the number of pizzas with a fixed budget and breadstick order

Calculate the cost of pizzas and breadsticks: Cost of pizzas: $5 \times \$7.69 = \$38.45$ Cost of breadsticks: $3 \times \$3.49 = \$10.47$ Subtotal: $\$38.45 + \$10.47 = \$48.92$

Add the delivery fee: $\$48.92 + \$3.00 = \$51.92$