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Mary intends to sell cups of coffee at the local taxi rank for extra money. She has organized to set up her stall at R40 per day and her traveling costs are R14.20 per day. Mary decided to exclude the cost of water when calculating the cost price per cup of coffee. The table below shows how Mary calculated the cost price of ONE cup of coffee.

\begin{tabular}{|c|c|c|c|}
\hline
\begin{tabular}{l}
QUANTITY \\
BOUGHT
\end{tabular} & \begin{tabular}{l}
COST OF \\
INGREDIENTS
\end{tabular} & \begin{tabular}{l}
AMOUNT USED \\
FOR ONE CUP
\end{tabular} & \begin{tabular}{l}
COST PER CUP OF \\
COFFEE
\end{tabular} \\
\hline 1 kg Coffee & R 97.95 & 0.04 kg & A \\
\hline 1 l Milk & R 11.99 & B & R 1.20 \\
\hline 2.5 kg Sugar & R 33.20 & 0.01 kg & R 0.13 \\
\hline 2 Foam Cups & R 1.78 & ONE & R 1.78 \\
\hline 50 Spoons & R 12.75 & ONE & R 0.26 \\
\hline TOTAL COST & & & C \\
\hline
\end{tabular}

1. Explain the meaning of the term "cost price."
2. Calculate the values of A, B, and C.

Sagot :

GinnyAnswer
Sure, let's break this down step by step:

### Explanation of the Cost Price
1. Explain the meaning of the word cost price.

The cost price refers to the total amount of money it costs to produce one unit of a product. This includes the cost of all materials, labor, and overhead expenses directly associated with the production. In this context, it is the total cost of all ingredients and packing materials required to produce one cup of coffee.

### Calculation of Values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]
2. Now calculate the values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].

#### Calculation of [tex]\(A\)[/tex], the cost of coffee per cup:
- The cost of 1 kg coffee is [tex]\( R 97.95 \)[/tex].
- The amount of coffee used per cup is [tex]\( 0.04 \)[/tex] kg.

To calculate the cost per cup of coffee:
[tex]\[ A = \frac{\text{cost of 1 kg coffee} \times \text{amount of coffee per cup}}{\text{unit conversion}} = 97.95 \times 0.04 = R 3.918 \][/tex]

So, [tex]\( A = R 3.918 \)[/tex].

#### Calculation of [tex]\(B\)[/tex], the amount of milk used per cup:
- The cost of 1 liter of milk is [tex]\( R 11.99 \)[/tex].
- The cost of milk per cup is [tex]\( R 1.20 \)[/tex].

To find the amount of milk used per cup:
[tex]\[ B = \frac{\text{cost of milk per cup}}{\text{cost of 1 liter of milk}} = \frac{1.20}{11.99} \approx 0.10008 \text{ liters} \][/tex]

So, [tex]\( B \approx 0.10008 \)[/tex] liters.

#### Calculation of [tex]\(C\)[/tex], the total cost per cup of coffee:
We add up the costs of all the components used per cup:

- Cost of coffee per cup: [tex]\( R 3.918 \)[/tex]
- Cost of milk per cup: [tex]\( R 1.20 \)[/tex]
- Cost of sugar per cup: [tex]\( R 0.13 \)[/tex]
- Cost of one foam cup: [tex]\( R 1.78 \)[/tex]
- Cost of one spoon: [tex]\( R 0.26 \)[/tex]

To calculate the total cost per cup:
[tex]\[ C = 3.918 + 1.20 + 0.13 + 1.78 + 0.26 = R 7.153332 \][/tex]

So, [tex]\( C = R 7.153332 \)[/tex].

#### Summary:
1. Cost price refers to the total cost of producing one unit of product.
2. The calculated values are:
- [tex]\( A \)[/tex] = [tex]\( R 3.918 \)[/tex]
- [tex]\( B \)[/tex] = approximately [tex]\( 0.10008 \)[/tex] liters
- [tex]\( C \)[/tex] = [tex]\( R 7.153332 \)[/tex]
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