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9.7: Yummy Yogurt

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Yummy’s sells yogurt desserts. Can you use the information in the sign to complete the table? Can you write a rule to represent the relationship between number of scoops and total cost? In this concept, we will practice making tables and writing rules to match given information.

Guidance

In order to make a table and write a rule for situations like the one above, we can use the problem solving steps to help.

• First, describe what you know. What does each scoop cost? What does the other part of the yogurt dessert cost?
• Second, identify what your job is. In these problems, your job will be to make a table and write a rule.
• Third, make a plan . In these problems, your plan should be to use the facts on the sign to fill in the table. Then, look for a pattern to help you write the rule.
• Fourth, solve . Implement your plan.
• Fifth, check . Make sure your rule works with the facts on the sign.

Example A

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 $\textbf{\textit{s}}$ for number of scoops and $\textbf{\textit{T}}$ for total cost.

Solution:

We can use problem solving steps to help us to fill in the table and write the rule.

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

Number of Scoops Total Cost
1 $\2.50$
2 $\4.00$
3 $\5.50$
4 $\7.00$

$\text{Rule}: \textbf{\textit{T}} \textbf{ \ = \1.50}\textbf{\textit{s}} \textbf{\ + \1.00} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$

$& \mathbf{Check:} && \text{Use the rule to verify the table.} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \\\\& && \1.50 \times 1 + \1.00 = \2.50 \\& && \1.50 \times 2 + \1.00 = \4.00 \\& && \1.50 \times 3 + \1.00 = \5.50 \\& && \1.50 \times 4 + \1.00 = \7.00$

Example B

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 $\textbf{\textit{p}}$ for number of scoops and $\textbf{\textit{M}}$ for total cost.

Solution:

We can use problem solving steps to help us to fill in the table and write the rule.

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

Number of Scoops Total Cost
1 $\5.75$
2 $\8.75$
3 $\11.75$
4 $\14.75$

$\text{Rule}: \textbf{\textit{M}} \textbf{ \ = \3.00}\textbf{\textit{p}} \textbf{\ + \2.75} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$

$& \mathbf{Check:} && \text{Use the rule to verify the table.} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \\\\& && \3.00 \times 1 + \2.75 = \5.75 \\& && \3.00 \times 2 + \2.75 = \8.75 \\& && \3.00 \times 3 + \2.75 = \11.75 \\& && \3.00 \times 4 + \2.75 = \14.75$

Example C

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 $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{L}}$ for total cost.

Solution:

We can use problem solving steps to help us to fill in the table and write the rule.

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

Number of Scoops Total Cost
1 $\3.50$
2 $\5.50$
3 $\7.50$
4 $\9.50$

$\text{Rule}: \textbf{\textit{L}} \textbf{ \ = \2.00}\textbf{\textit{n}} \textbf{\ + \1.50} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$

$& \mathbf{Check:} && \text{Use the rule to verify the table.} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \\\\& && \2.00 \times 1 + \1.50 = \3.50 \\& && \2.00 \times 2 + \1.50 = \5.50 \\& && \2.00 \times 3 + \1.50 = \7.50 \\& && \2.00 \times 4 + \1.50 = \9.50$

Concept Problem Revisited

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 $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{T}}$ for total cost.

We can use problem solving steps to help us to fill in the table and write the rule.

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

Number of Scoops Total Cost
1 $\3.00$
2 $\5.00$
3 $\7.00$
4 $\9.00$

$\text{Rule}: \textbf{\textit{T}} \textbf{ \ = \2.00}\textbf{\textit{n}} \textbf{\ + \1.00} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$

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

Vocabulary

One type of table shows a relationship between an input and an output . In this concept, the inputs of our tables were number of scoops and the outputs of our tables were total cost. A rule is an equation that can describe the relationship between the inputs and the outputs of a table. In this concept, we wrote rules that showed the relationship between the number of scoops and the total cost.

Guided Practice

1. 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 $\textbf{\textit{b}}$ for number of scoops and $\textbf{\textit{C}}$ for total cost.

2. 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 $\textbf{\textit{t}}$ for number of scoops and $\textbf{\textit{R}}$ for total cost.

3. 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 $\textbf{\textit{q}}$ for number of scoops and $\textbf{\textit{V}}$ for total cost.

1. a.

Number of Scoops Total Cost
1 $\3.25$
2 $\4.50$
3 $\5.75$
4 $\7.00$

b. Rule: $\mathbf{C} = \1.25\textbf{\textit{b}} + \2.00$

2. a.

Number of Scoops Total Cost
1 $\4.50$
2 $\7.50$
3 $\10.50$
4 $\13.50$

b. Rule: $\textbf{\textit{R}} = \3.00\textbf{\textit{t}} + \1.50$

3. a.

Number of Scoops Total Cost
1 $\4.00$
2 $\5.25$
3 $\6.50$
4 $\7.75$

b. Rule: $\textbf{\textit{V}} = \1.25\textbf{\textit{q}} + \2.75$

Practice

1. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.
2. Write a rule to represent the relationship between number of scoops and total cost. Use $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{C}}$ for total cost.

Yummy's sells apple pie yogurt.

1. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.
2. Write a rule to represent the relationship between number of scoops and total cost. Use $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{C}}$ for total cost.

Yummy's sells cheesecake yogurt.

1. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.
2. Write a rule to represent the relationship between number of scoops and total cost. Use $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{C}}$ for total cost.

Yummy's sells s'mores yogurt.

1. Use the information in the sign. Complete the table to show how total cost is related to number of scoops.
2. Write a rule to represent the relationship between number of scoops and total cost. Use $\textbf{\textit{n}}$ for number of scoops and $\textbf{\textit{C}}$ for total cost.

Jan 18, 2013

May 27, 2014