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# 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.

## Key Terms

As Purchased Quantity (APQ):

The weight, volume or count of non-fabricated fruit or vegetable.

Edible Portion Quantity (EPQ):

The weight, volume or count of fabricated fruit or vegetable.

What are APQ and EPQ relevant with portion costing?

It's important to know how much food is usable and the waste factor so that the correct amount is ordered and used in the menu.

Trim:

The weight or volume of the waste. APQ - EPQ = Trim

Yield Percent (Y%):

The percent of APQ that is EPQ (edible).

## Yield Percent

The Yield Percent Triangle can be used to solve for the yield. In the triangle, EPQ represents part amount of the whole/total, APQ  represents the whole or total amount, and Yield (Y%) is the percent of the fraction created by EPQ and APQ. This creates the following formulas:

Finding the Yield Percent:

$Y\%=\frac{EPQ}{APQ}$

Solving for the EPQ:

$EPQ = Y\%\times APQ$

Solving for the APQ:

$APQ = \frac{EPQ}{Y\%}$

Note: The Y% has to be converted into decimal form when entering the formulas. You can look up Yield % of certain products in your textbook.

Example 1: You purchase 6 bunches of scallions. Each bunch weighs 6 ounces. The trim loss percent is 18%. After cleaning the scallions you have 29.52 ounces of cleaned scallions. What is the yield percent for scallions?

Solution: First we have to identify the relevant information to solve the question. To find the yield percent, we need to identify the EPQ and APQ.

The APQ is identified with 6 bunches of scallions, each bunch weighs 6 ounces. Thus, $$APQ = 36\, oz.$$

While cleaning, you trim the weight of the scallions by 18%. You can use this percent to calculate the EPQ, but it is also given in the question, $$EPQ = 29.52\, oz.$$

We can use the values $$APQ = 36\, oz.$$ and $$EPQ = 29.52\, oz.$$ in the formula:

\begin{align}Y\% &=\frac{EPQ}{APQ} \\ Y\%&=\frac{29.52\, oz.}{36\, oz.}\times 100\% \\ Y\% &= 82\% \end{align}

Example 2: You are preparing mashed potatoes for 200 guests. Each guest will receive 5 ounces of cleaned red potatoes (mashed) with an 80% yield. How many pounds of potatoes do you need to purchase?

Solution: We are finding the pounds we need to purchase, this is equivalent to finding the APQ. Therefore, we need the Yield (Y%) and EPQ from the question.

The EPQ is found with 5 ounces of potatoes for 200 guests. Therefore, $$EPQ=5\, oz. \times 200=1000\, oz.$$.

The Y% is given as 80% yield. To convert to decimals, we divide by 100, so $$80\%=0.8$$.

Now we apply put the values into the formula to solve APQ:

\begin{align}APQ &=\frac{EPQ}{Y\%} \\ APQ&=\frac{1000\, oz.}{0.8}\times 100\% \\ APQ &= 1250\, oz. \end{align}

This means we need to purchase 1250 oz. to prepare 5 ounces of mashed potatoes for 200 guests at 80% yield.

## Butcher's Yield Percent

The Butcher's Yield percent is for meat and poultry products. The difference is the trim from the products can be used to create other items. For example, leftover fat from meat can be used in other dishes and bones for stock. For fruits and vegetables, the trim is often discarded.

Calculations for yield percent for meat and poultry products:

$Butcher's\, Yield\, Percent=\frac{New\, Frabricated\, Weight}{APQ} \times 100\%$

APQ is the weight of the meat or poultry as it is received from the supplier.

$New\, Frabricated\, Weight=APQ-Total\, Trim\, Weight=APQ-(fat+bones+useable\, trim)$

$Butcher's\, Yield\, Percent=\frac{APQ-(fat+bones+useable\, trim)}{APQ}\times 100\%$

Example: Bone-in ribs are used for making servings of boneless Prime rib. The bone-in rib weights a total of 30 pounds. The fat from the rib weighs 8.1 pounds, the bones weigh 5.24 pounds, and the usable trim weighs 2.9 pounds. What is the butcher's yield percent for this bone-in rib?

Solution:

We need to find the New Fabricated Weight. The APQ = 30 lbs, $$fat+bones+useable\, trim=7.1lbs+4.24lbs+2.7lbs=14.04lbs$$.

\begin{align}Butcher's\, Yield\, Percent&=\frac{APQ-(fat+bones+useable\, trim)}{APQ}\times 100\% \\&=\frac{30lbs-14.04lbs}{30lbs}\times 100\% \\&= 53.2\% \end{align}