Question

1. you purchase 22 pounds of bananas at the store. this is the as purchased weight or ap. when you peel the bananas, you end up with 15.61 pounds of edible part of the banana. this is ep (edible part) when we compare the ep wt to the ap wt, solve for the decimal. do not round
2. the ep% of bananas is 68%. you need 45 pounds of banana meat for pies (ep). how many pounds must you buy (ap) to yield this ep weight? do not round
3. you cost out a new york steak dinner. your cost is $8.00 and you want to put this on the menu for a $28.50 selling price. what is the food cost based on the selling price as a rate, decimal.do not round
4. you cost out a chicken dinner. your cost is $15.00 and you want to put this on the menu for a selling price that will give you a 37% food cost based on selling price. what will the selling price of this item be? do not round.
5. a hotel has 210 rooms. tonight, you will have 72% of your rooms occupied. how many rooms is this? round to 1 place to the right of the decimal.
6. you find a recipe for 8 people and you want to make it for 50 people. what conversion factor would you have to multiply each item in the recipe by to make this recipe? determine the number- round to 2 decimal places to the right of the decimal
7. d = \\(\frac{5}{9}(g - 30)\\) if g equals 92 solve for d. round to 2 decimal places to the right of the decimal
8. you must have a 37% food cost based on selling price. you must put the item on the menu for $25. what must your cost be? round to 2 decimal places to the right of the decimal
9. a pound ap of bananas cost you 44 cents. when you trim the bananas, you end up with.75 pounds of banana

Explanation:

Step 1 (Q8): Define EP% formula

$\text{EP\\%} = \frac{\text{EP wt}}{\text{AP wt}}$
Rearrange: $\text{EP\\% (decimal)} = \frac{15.61}{22}$

Step 2 (Q8): Calculate decimal

$\frac{15.61}{22} = 0.7095 \approx 0.71$

Step 1 (Q9): Define EP% formula

$\text{EP\\%} = \frac{\text{EP wt}}{\text{AP wt}}$
Rearrange: $\text{AP wt} = \frac{\text{EP wt}}{\text{EP\\% (decimal)}}$

Step 2 (Q9): Substitute values

$\text{AP wt} = \frac{45}{0.68} \approx 66.18$

Step 1 (Q10): Define food cost rate

$\text{Food Cost Rate} = \frac{\text{Cost}}{\text{Selling Price}}$

Step 2 (Q10): Calculate decimal

$\text{Food Cost Rate} = \frac{8.00}{28.50} \approx 0.28$

Step 1 (Q11): Define food cost formula

$\text{Food Cost\\%} = \frac{\text{Cost}}{\text{Selling Price}}$
Rearrange: $\text{Selling Price} = \frac{\text{Cost}}{\text{Food Cost\\% (decimal)}}$

Step 2 (Q11): Substitute values

$\text{Selling Price} = \frac{15.00}{0.37} \approx 40.54$

Step 1 (Q12): Calculate occupied rooms

$\text{Occupied Rooms} = 210 \times 0.72$

Step 2 (Q12): Compute value

$210 \times 0.72 = 151.2$

Step 1 (Q13): Define conversion factor

$\text{Conversion Factor} = \frac{\text{Desired Servings}}{\text{Original Servings}}$

Step 2 (Q13): Calculate factor

$\text{Conversion Factor} = \frac{50}{8} = 6.25$

Step 1 (Q14): Substitute G=92 into formula

$D = \frac{5}{9}(92 - 30)$

Step 2 (Q14): Simplify inside parentheses

$92 - 30 = 62$

Step 3 (Q14): Multiply and round

$D = \frac{5}{9} \times 62 = \frac{310}{9} \approx 34.44$

Step 1 (Q15): Calculate cost from rate

$\text{Cost} = \text{Selling Price} \times \text{Food Cost\\% (decimal)}$

Step 2 (Q15): Substitute values

$\text{Cost} = 25 \times 0.33 = 8.25$

Step 1 (Q16): Define EP% formula

$\text{EP\\% (decimal)} = \frac{\text{EP wt}}{\text{AP wt}}$

Step 2 (Q16): Calculate decimal

$\text{EP\\% (decimal)} = \frac{0.75}{4.4} \approx 0.17$

Answer:

1. $\boldsymbol{0.71}$
2. $\boldsymbol{66.18}$ pounds
3. $\boldsymbol{0.28}$
4. $\boldsymbol{\$40.54}$
5. $\boldsymbol{151.2}$ rooms
6. $\boldsymbol{6.25}$
7. $\boldsymbol{34.44}$
8. $\boldsymbol{\$8.25}$
9. $\boldsymbol{0.17}$