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9.13: Yummy Yogurt and Yummy Yogurt Extra for Experts

Difficulty Level: At Grade Created by: CK-12

Yummy Yogurt – Write Function Rules

Notes to Teachers

Students use facts on signs to complete tables of related data. They use variables to write rules that relate Number of Scoops to Total Cost. All functions are of the form y=n(a)+b\begin{align*}y = n(a) + b\end{align*}. In that function, \begin{align*}\textbf{\textit{y}}\end{align*} represents the total cost of a cone of yogurt. The total cost is the sum of the cost of the cone or some other fixed item \begin{align*}\textbf{(\textit{b})}\end{align*} and the product of the number of scoops \begin{align*}(n)\end{align*}, which varies, and the cost of one scoop \begin{align*}\textbf{(\textit{a})}\end{align*}.

Solutions

Yummy Yogurt 1

a.

Number of Scoops Total Cost
1 \begin{align*}\4.50\end{align*}
2 \begin{align*}\6.00\end{align*}
3 \begin{align*}\7.50\end{align*}
4 \begin{align*}\9.00\end{align*}

b. Rule: \begin{align*}\mathbf{T} = \1.50\textbf{\textit{s}} + \3.00\end{align*}

Yummy Yogurt 2

a.

Number of Scoops Total Cost
1 \begin{align*}\5.75\end{align*}
2 \begin{align*}\8.75\end{align*}
3 \begin{align*}\11.75\end{align*}
4 \begin{align*}\14.75\end{align*}

b. Rule: \begin{align*}\mathbf{T} = \3.00\textbf{\textit{p}} + \2.75\end{align*}

Yummy Yogurt 3

a.

Number of Scoops Total Cost
1 \begin{align*}\3.50\end{align*}
2 \begin{align*}\5.50\end{align*}
3 \begin{align*}\7.50\end{align*}
4 \begin{align*}\9.50\end{align*}

b. Rule: \begin{align*}\mathbf{T} = \2.00\textbf{\textit{n}} + \1.50\end{align*}

Yummy Yogurt 4

a.

Number of Scoops Total Cost
1 \begin{align*}\3.25\end{align*}
2 \begin{align*}\4.50\end{align*}
3 \begin{align*}\5.75\end{align*}
4 \begin{align*}\7.00\end{align*}

b. Rule: \begin{align*}\mathbf{T} = \1.25\textbf{\textit{b}} + \2.00\end{align*}

Yummy’s sells yogurt desserts.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{n}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{T}}\end{align*} for total cost.

\begin{align*}& \mathbf{Describe:} && \text{The sign shows the cost of a cone and the cost of one scoop of yogurt}. \\ & && \text{The table has two columns, one for number of scoops and the other for total cost}. \\ \\ & \mathbf{My \ Job:} && \text{Complete the table for}\ 1\ \text{through}\ 4\ \text{scoops of yogurt. Write a function rule} \\ & && \text{to show how total cost is related to number of scoops and the cost of the cone}. \\ \\ & \mathbf{Plan:} && \text{Start with the table. Remember to include the cost of the cone in the total} \\ & && \text{cost. Then write the rule}. \\ \\ & \mathbf{Solve:} \end{align*}

Number of Scoops Total Cost
1 \begin{align*}\3.00\end{align*}
2 \begin{align*}\5.00\end{align*}
3 \begin{align*}\7.00\end{align*}
4 \begin{align*}\9.00\end{align*}

\begin{align*}\text{Rule}: \textbf{\textit{T}} \textbf{ \ = \2.00}\textbf{\textit{n}} \textbf{\ + \1.00} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\end{align*}

\begin{align*}& \mathbf{Check:} && \text{Use the rule to verify the table.} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \\ \\ & && \2.00 \times 1 + \1.00 = \3.00 \\ & && \2.00 \times 2 + \1.00 = \5.00 \\ & && \2.00 \times 3 + \1.00 = \7.00 \\ & && \2.00 \times 4 + \1.00 = \9.00\end{align*}

Yummy Yogurt 1 – Write Function Rules

Celeste’s sells yogurt sundaes.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{s}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{T}}\end{align*} for total cost.

Yummy Yogurt 2 – Write Function Rules

Delicioso’s sells yogurt banana splits.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{p}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{M}}\end{align*} for total cost.

Yummy Yogurt 3 – Write Function Rules

Flavor’s sells yogurt floats.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{n}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{L}}\end{align*} for total cost.

Yummy Yogurt 4 – Write Function Rules

Yaley’s sells yogurt chocolate cups.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{b}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{C}}\end{align*} for total cost.

Extra for Experts: Yummy Yogurt – Write Function Rules

Solutions

Extra for Experts: Yummy Yogurt 1

a.

Number of Scoops Total Cost
1 \begin{align*}\4.50\end{align*}
2 \begin{align*}\7.50\end{align*}
3 \begin{align*}\10.50\end{align*}
4 \begin{align*}\13.50\end{align*}

b. Rule: \begin{align*}\textbf{\textit{R}} = \3.00\textbf{\textit{t}} + \1.50\end{align*}

Extra for Experts: Yummy Yogurt 2

a.

Number of Scoops Total Cost
1 \begin{align*}\4.00\end{align*}
2 \begin{align*}\5.25\end{align*}
3 \begin{align*}\6.50\end{align*}
4 \begin{align*}\7.75\end{align*}

b. Rule: \begin{align*}\textbf{\textit{V}} = \1.25\textbf{\textit{q}} + \2.75\end{align*}

Extra for Experts: Yummy Yogurt 1 – Write Function Rules

Mixer’s sells yogurt slushes.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{t}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{R}}\end{align*} for total cost.

Extra for Experts: Yummy Yogurt 2 – Write Function Rules

Fabulous’s sells yogurt sandwiches.

a. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.

b. Write a rule to represent the relationship between number of scoops and total cost. Use \begin{align*}\textbf{\textit{q}}\end{align*} for number of scoops and \begin{align*}\textbf{\textit{V}}\end{align*} for total cost.

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Date Created:
Feb 23, 2012