Math Problem Statement

Find the missing values of A and B. Remember to show your calculations. Table data provided.

Solution

To solve this table, we need to determine the values of AA and BB, following the relationship between the number of items and their cost. Based on the data, this relationship appears to be proportional.

Step 1: Confirm proportionality

  • For 5 items, the cost is 2020. This gives a cost per item of: Cost per item=205=4R per item.\text{Cost per item} = \frac{20}{5} = 4 \, \text{R per item}.

  • Similarly, for 10 items, the cost is 4040: Cost per item=4010=4R per item.\text{Cost per item} = \frac{40}{10} = 4 \, \text{R per item}.

Since the cost per item is constant (4R per item4 \, \text{R per item}), we can conclude that the relationship is proportional.


Step 2: Calculate AA (cost for 7 items)

The cost for 7 items is: A=7×4=28R.A = 7 \times 4 = 28 \, \text{R}.


Step 3: Calculate BB (number of items for 60 R)

To find BB, we solve: B=Total CostCost per item=604=15items.B = \frac{\text{Total Cost}}{\text{Cost per item}} = \frac{60}{4} = 15 \, \text{items}.


Final Table

\hline \text{No. of Items} & 5 & 7 & 10 & 15 \\ \hline \text{Cost (R)} & 20 & 28 & 40 & 60 \\ \hline \end{array}$$ --- Let me know if you'd like further details or have additional questions! ### Related Questions 1. What is the general formula for finding cost given the number of items? 2. How can you determine if a relationship is proportional? 3. What happens if the cost per item changes? How would you adjust the calculations? 4. Can this type of proportional relationship be represented graphically? If yes, how? 5. How would you solve this problem if only partial information (e.g., just $$A$$) was given? ### Tip Always check if the relationship between two quantities is proportional by dividing one by the other to confirm if the ratio remains constant!

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Math Problem Analysis

Mathematical Concepts

Proportionality
Ratios
Basic Arithmetic

Formulas

Cost per item = Total cost / Number of items
Total cost = Number of items × Cost per item

Theorems

Proportional Relationship Theorem

Suitable Grade Level

Grades 6-8