Login
Premium
Home Question Bank Math Algebra
Question
upstudy study bank question image url

(2) A large plzzs at Papa's Ptzzerla costs \( \$ 6,80 \) plus \( \$ 0,90 \) for each topping. The cost of a large clicuse plzza at Mama's Pizzals \( \$ 7.30 \) plus \( \$ 0.65 \) lor each topping. Which system of equations could be used to determine how many topplags you need to add to a large cheese pizza from Papa's'Pizzeria and Mama's Plazs in onder for the pigas to cost the same, not including tax?

Ask by Hodgson Ford. in the United States
Jan 27,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Let \( y \) be the total cost and \( x \) be the number of toppings. Then, the system of equations is: \[ \begin{cases} y = 6.80 + 0.90x \\ y = 7.30 + 0.65x \end{cases} \]

Solution

To determine the number of toppings \( x \) needed for the large pizzas from Papa's Pizzeria and Mama's Pizzas to cost the same, we can set up a system of equations based on their pricing structures. 1. **Cost at Papa's Pizzeria:** \[ \text{Cost}_\text{Papa} = 6.80 + 0.90x \] - **$6.80**: Base cost for a large pizza. - **$0.90x**: Additional cost per topping. 2. **Cost at Mama's Pizzas:** \[ \text{Cost}_\text{Mama} = 7.30 + 0.65x \] - **$7.30**: Base cost for a large pizza. - **$0.65x**: Additional cost per topping. 3. **Setting the Costs Equal:** Since we want both pizzas to cost the same, set the two equations equal to each other: \[ 6.80 + 0.90x = 7.30 + 0.65x \] **System of Equations:** \[ \begin{cases} \text{Cost}_\text{Papa} = 6.80 + 0.90x \\ \text{Cost}_\text{Mama} = 7.30 + 0.65x \\ 6.80 + 0.90x = 7.30 + 0.65x \end{cases} \] This system allows you to solve for \( x \), the number of toppings needed for both pizzas to have the same total cost. **Solution Steps:** 1. Subtract \( 6.80 \) from both sides: \[ 0.90x = 0.50 + 0.65x \] 2. Subtract \( 0.65x \) from both sides: \[ 0.25x = 0.50 \] 3. Divide both sides by \( 0.25 \): \[ x = 2 \] So, **2 toppings** are needed for both pizzas to cost the same. **Final Answer:** Let y = cost and x = toppings. Then  y = 6.80 + 0.90 x  y = 7.30 + 0.65 x is a suitable system of equations.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Bonus Knowledge

To find the number of toppings that make the pizzas cost the same, we can set up the following equations based on the given prices. For Papa's Pizzeria, the equation is \( C_1 = 6.80 + 0.90t \) where \( C_1 \) is the cost and \( t \) is the number of toppings. For Mama's Pizzeria, we have \( C_2 = 7.30 + 0.65t \). To find when these costs are equal, we set the two equations equal to each other: \( 6.80 + 0.90t = 7.30 + 0.65t \). You might have fun experimenting with different scenarios, such as trying out different numbers of toppings and calculating the costs to see where the balance strikes! Doing this on a spreadsheet can give you instant feedback and even help you discover if one pizzeria offers better value as you pile on the toppings!

Related Questions

7. Efectueaza sis scrie rezultatul sub formă de putere: \( \begin{array}{lll}\text { a) } \frac{18}{5} \cdot\left(\frac{18}{5}\right)^{2}= & \text { b) }\left(\frac{6}{5}\right)^{2} \cdot\left(\frac{6}{5}\right)^{3} \cdot \frac{6}{5}= & \text { c) }\left(\frac{19}{5}\right)^{5} \cdot\left(\frac{19}{5}\right)^{16}= \\ \begin{array}{lll}\text { d) } \frac{3}{2} \cdot\left(\frac{3}{2}\right)^{3} \cdot\left(\frac{3}{2}\right)^{0} \cdot\left(\frac{3}{2}\right)^{4}= & \text { e) }\left[\left(\frac{28}{5}\right)^{2}\right]^{3}= & \text { f) }\left[\left(\frac{5}{6}\right)^{6}\right]^{7}= \\ \text { g) }\left[\left(\frac{24}{5}\right)^{2} \cdot\left(\frac{24}{5}\right)^{3}\right]^{8}= & \text { h) }\left[\frac{5}{7} \cdot\left(\frac{5}{7}\right)^{0} \cdot\left(\frac{5}{7}\right)^{4}\right]^{5}= & \text { i) }\left(\frac{29}{10}\right)^{10}:\left(\frac{29}{10}\right)^{7}=\end{array} \\ \left.\left.\begin{array}{lll}\text { j) }\left(\frac{1}{3}\right)^{17}: \frac{1}{3}= & \left.\text { k) }\left(\frac{3}{7}\right)^{11} \cdot\left(\frac{9}{49}\right)^{3}:\left(\frac{3}{7}\right)^{15}=1\right)\end{array}\right]\left(1 \frac{1}{2}\right)^{2}\right]^{8}:\left(\frac{3}{2}\right)^{13}= \\ \text { m) }\left(\frac{9}{10}\right)^{7} \cdot\left(\frac{1}{5}\right)^{7}= & \text { n) }\left(\frac{5}{2}\right)^{10} \cdot\left(\frac{8}{5}\right)^{10}: 2^{10}= & \text { o) } 9^{3} \cdot\left(\frac{7}{10}\right)^{3}:\left(\frac{63}{10}\right)^{3}= \\ \text { p) }\left[\left(\frac{1}{5}\right)^{7}\right]^{2} \cdot 6^{14}:\left(\frac{6}{5}\right)^{14}= & \text { q) }\left(\frac{5}{2}\right)^{7}:\left(\frac{5}{2}\right)^{5}= & \end{array} \)
Algebra Romania Jan 30, 2025
A. \( 3 x^{2}-x-10 \)
Algebra United Arab Emirates Jan 30, 2025
Oppgave 3.113 Bruk stigningstallet og konstantleddet til å tegne linjene. \( \begin{array}{ll}\text { a) } y=2 x-6 & \text { b) } y=-2 x+4\end{array} \) \( \begin{array}{ll}\text { c) } y=\frac{1}{4} x-1 & \text { d) } y=-\frac{5}{2} x+\frac{7}{2} \\ \text { av det tor to }\end{array} \)
Algebra Norway Jan 30, 2025
Simplify: \( \left(\frac{1447^{\frac{-3}{4}} 8^{\frac{2}{7}} \sqrt[6]{x^{5}} \sqrt[5]{y^{3}} \sqrt[7]{8}}{12^{12} 8^{12} 7^{2} x^{\frac{4}{5}} \sqrt[3]{y^{5} z^{\frac{2}{6}}}}+\frac{x^{\frac{-9}{4}} y^{\frac{2}{7}} z^{\frac{-0}{5}} s^{\frac{3}{2}}}{x^{2} y^{5} z^{\frac{2}{6}} s^{-9}}\right)^{\frac{4}{4}} \)
Algebra United Arab Emirates Jan 30, 2025
A. \( 3 x^{2}-x-10 \)
Algebra United Arab Emirates Jan 30, 2025

Latest Algebra Questions

7. Efectueaza sis scrie rezultatul sub formă de putere: \( \begin{array}{lll}\text { a) } \frac{18}{5} \cdot\left(\frac{18}{5}\right)^{2}= & \text { b) }\left(\frac{6}{5}\right)^{2} \cdot\left(\frac{6}{5}\right)^{3} \cdot \frac{6}{5}= & \text { c) }\left(\frac{19}{5}\right)^{5} \cdot\left(\frac{19}{5}\right)^{16}= \\ \begin{array}{lll}\text { d) } \frac{3}{2} \cdot\left(\frac{3}{2}\right)^{3} \cdot\left(\frac{3}{2}\right)^{0} \cdot\left(\frac{3}{2}\right)^{4}= & \text { e) }\left[\left(\frac{28}{5}\right)^{2}\right]^{3}= & \text { f) }\left[\left(\frac{5}{6}\right)^{6}\right]^{7}= \\ \text { g) }\left[\left(\frac{24}{5}\right)^{2} \cdot\left(\frac{24}{5}\right)^{3}\right]^{8}= & \text { h) }\left[\frac{5}{7} \cdot\left(\frac{5}{7}\right)^{0} \cdot\left(\frac{5}{7}\right)^{4}\right]^{5}= & \text { i) }\left(\frac{29}{10}\right)^{10}:\left(\frac{29}{10}\right)^{7}=\end{array} \\ \left.\left.\begin{array}{lll}\text { j) }\left(\frac{1}{3}\right)^{17}: \frac{1}{3}= & \left.\text { k) }\left(\frac{3}{7}\right)^{11} \cdot\left(\frac{9}{49}\right)^{3}:\left(\frac{3}{7}\right)^{15}=1\right)\end{array}\right]\left(1 \frac{1}{2}\right)^{2}\right]^{8}:\left(\frac{3}{2}\right)^{13}= \\ \text { m) }\left(\frac{9}{10}\right)^{7} \cdot\left(\frac{1}{5}\right)^{7}= & \text { n) }\left(\frac{5}{2}\right)^{10} \cdot\left(\frac{8}{5}\right)^{10}: 2^{10}= & \text { o) } 9^{3} \cdot\left(\frac{7}{10}\right)^{3}:\left(\frac{63}{10}\right)^{3}= \\ \text { p) }\left[\left(\frac{1}{5}\right)^{7}\right]^{2} \cdot 6^{14}:\left(\frac{6}{5}\right)^{14}= & \text { q) }\left(\frac{5}{2}\right)^{7}:\left(\frac{5}{2}\right)^{5}= & \end{array} \)
Algebra Romania Jan 30, 2025
B. \( x^{2}-3 x-28 \)
Algebra United Arab Emirates Jan 30, 2025
A. \( 3 x^{2}-x-10 \)
Algebra United Arab Emirates Jan 30, 2025
A. \( 3 x^{2}-x-10 \)
Algebra United Arab Emirates Jan 30, 2025
lify: \( \left(\frac{1447^{\frac{-3}{4}} 8^{\frac{2}{7}} \sqrt[6]{x^{5}} \sqrt[5]{y^{3}} \sqrt[7]{z}}{12^{12} 8^{12} 7^{2} x^{\frac{4}{5}} \sqrt[3]{y^{5}} z^{\frac{2}{6}}} * \frac{x^{\frac{-3}{4}} y^{\frac{2}{7}} z^{\frac{-8}{5}} s^{\frac{3}{2}}}{x^{2} y^{5} z^{\frac{2}{6}} s^{-9}}\right)^{\frac{7}{4}} \)
Algebra United Arab Emirates Jan 30, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy