# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Definitions

Cost per Unit

The cost per unit (often denoted cost/unit) is the cost of one unit of whatever is being purchased. This could be:

• the cost of one apple (cost per one apple or “cost/apple”) ,
• the cost of one pound of flour (cost per pound or “cost/pound”), or
• the cost of one kg of dates (cost per kg or "cost/kg")

We can use the following formula to calculate cost per unit:

$$Cost/Unit = \frac{As-Purchased \ Cost}{Total \ number \ of \ units}$$,

where As-Purchased Cost (APC) is the cost paid to the supplier for the as-purchased quantity (APQ) of products you purchase. To review APQ, visit our Yield Percent page.

Total Cost

When we have calculated the Cost/Unit, we can use it to determine the Total Cost using the general formula:

$$Total \ Cost = Number \ of \ Units \times Cost/Unit$$

Note: The units used in 'Number of Units' and 'Cost/Unit' must be the same. (For example, we can use the above formula to directly calculate the total cost of 4lbs of flour at $10/lb, but cannot use it for 4kgs of flour at$10/lb).

Edible Portion Cost (EPC)

The edible portion cost (EPC) is the cost per unit of the edible portion quantity (EPQ) of products purchased. To review EPQ, visit our Yield Percent page. To calculate EPC, we use the formula:

$$Edible \ Portion \ Cost = \frac{APC}{Yield \ Percentage}$$,

where $$Yield \ Percentage=\frac{APQ}{EPQ}$$ is expressed as a decimal.

Note: EPC is always equal to or greater than APC. If the purchased product from the supplier is used as is (e.g. flour, sugar, etc.), then $$APC=EPC$$. Otherwise, if further processing or cleaning is required (e.g. vegetables, meats, etc.), then $$APC<EPC$$.

## Examples

Example 1 - Cost per Unit

If you are looking for corn in a weekly grocery flyer and it shows that the price for two corns is $4.00, what is the cost per corn? Solution We see that if two corns cost$4.00, then one corn should cost half of that amount, $2.00. In this case, one unit is one corn, so using the cost per unit formula, we have the calculation: $$Cost/Corn = 4.00 \div 2 \ corn= 2.00$$ So, the cost is$2.00 per corn (or $2.00/corn). Example 2 - Cost per Unit You are going to bake bread and need to buy flour. If one bag of flour is sold for$12.50 and each bag weighs 10 pounds, what is the cost per pound?

Solution

From the question, we know that the APC=$12.50 (per bag or 10 pounds of flour) and the total number of units is 10 (pounds). In this case, one unit is one pound, so substituting these values into the cost per unit formula gives: $$Cost/Pound = 12.50 \div 10 \ pounds = 1.25$$ So, the cost is$1.25 per pound of flour (or $1.25/pound). Example 1 - Total Cost ExampleYou purchase two bags of flour from the grocery store. If the cost of one bag is$12.00, what is the total cost of the flour you bought?

Solution

From the question, we know that the number of units purchased is 2 (bags) and the cost/unit is $12.00/bag. Since both values are in the same units (bag), we can directly calculate the total cost using the general formula as follows: $$Total \ Cost = 2 \ bags \times 12.00/bag = 24$$ So, the total cost for both bags of flour is$24.00.

Example 2 - Total Cost

You bought a box of oranges for $9.00. If each box contains 6 oranges, what is the total cost for 4 oranges? Solution From the question, we know that the number of units being purchased is 4 (oranges), but do not know the cost per unit (1 orange). Instead, we know that a box of 6 oranges costs$9.00, so we first determine the cost per unit using this information:

$$Cost/Orange = 9.00 \div 6 \ oranges = 1.50$$

Since both the number of units and the cost/unit are in the same units (oranges), we can directly calculate the total cost using the general formula as follows:

$$Total \ Cost = 4 \ oranges \times 1.50/orange = 6$$

So, the total cost for 4 oranges is $6.00. Example 3 - Total Cost Turmeric powder can be purchased in 250g containers for$12.00 each. How much would 1 kg of turmeric powder cost?

Solution

In this case, the units in the given problem are the not the same: cost per unit is in grams (g), while the number of units purchased is in kilograms (kg). So before using the total cost formula, we need to convert from one unit into the other:

$$1kg = 1000g$$

We also need to find the cost per unit:

$$Cost \ per \ unit = 12 \div 250g = 0.048/g$$

Finally, substituting the values we've found into the total cost formula gives:

$$Total \ Cost = 1000g \times 0.048/g = 48$$

So, the total cost for 1kg (or 1000g) of turmeric powder costs $48.00. Example 4 - Total Cost Apples are on sale at a price of$3.50 per 1kg. How much would 5 pounds of apples cost?

Solution

In this case, the units in the given problem are the not the same: cost per unit is in kilograms (kg), while the number of units purchased is in pounds (lbs). So before using the total cost formula, we need to convert from one unit into the other:

$$1kg = 2.20lbs$$

Substituting the information we've found and from the original question into the total cost formula gives:

$$Total \ Cost = 5\cancel{lbs} \times 3.50/2.20\cancel{lbs} = 7.95$$

(the pounds units cancel each other out)

So, the total cost for 5 pounds of apples costs $7.95. Example 1 - Edible Portion Cost (EPC) You purchased 25 pounds of corn for$35.00. After cleaning and peeling, if you have 15 pounds of corn remaining, calculate the edible portion cost.

Solution

We must first determine the the yield percentage using the following steps:

1. Identify the EPQ and APQ: From the question, we know that $$EPQ=15 \ pounds$$ and $$APQ=25 \ pounds$$.
2. Check the EPQ and APQ units: Both the APQ and EPQ are in pounds. If not, we would have to convert either one of the values to the same unit as the other.
3. Substitute EPQ and APQ values into the yield percentage formula:

$$Yield \ Percentage = \frac{15 \ pounds}{25 \ pounds}\times 100=60\%$$

Now, we can find the edible portion cost substituting the yield percentage of 0.6 (expressed as decimal) into the formula:

$$Edible \ Portion \ Cost: \frac{35.00}{0.6}=58.33$$

So, the edible portion cost of the corn is \$58.33.