Question

# Jamie will choose between two catering companies for an upcoming party. Company A charges a set up fee of $ 500 plus $25 for each guest. Company B charges a set up fee of $200 plus $ 30 per guest

a) Write expression that you can use to determine the amount each company charges for g guests .

b) Jamie learns that the $ 500 set up fee for company A includes payment for 20 guests. The $25 per guests charge is for every guest over the first 20.If there will be 50 guests , which company will cost the least ? Explain.

Hint:

### 1. Variable charges = Number of guests × price per guest

2. Total cost = Setup charges + Variable charges

## The correct answer is: From Equations vi & vii, we can conclude that Company A will cost the least.

### Step-by-step solution:-

a). As per the given information, we get-

Setup fees for Company A = $ 500

Variable charges for Company A = $ 25 per guest

Setup fees for Company B = $ 200

Variable charges for Company B = $ 30 per guest

Now, we know that-

For Company A-

Variable charges = Number of guests × price per guest

∴ Variable charges = g × 25 ................................................................................................... (From given information)

∴ Variable charges = 25g ....................................................................................................... (Equation i)

Amount charged for g guests = Setup charges + Variable charges

∴ Amount charged for g guests = 500 + 25g ......................... (From given information & Equation i) ............. (Equation ii)

For Company B-

Variable charges = Number of guests × price per guest

∴ Variable charges = g × 30 ................................................................................................... (From given information)

∴ Variable charges = 30g ....................................................................................................... (Equation iii)

Amount charged for g guests = Setup charges + Variable charges

∴ Amount charged for g guests = 200 + 30g ......................... (From given information & Equation iii) ............. (Equation iv)

b). As per the second situation,

Total number of guests = g = 50

Also,

Variable cost for company A = price per guest × (Number of guests - 20) ….................. (because setup fees includes charges for 20 guests)

∴ Variable cost for company A = 25 × (50 - 20)

∴ Variable cost for company A = 25 × 30

∴ Variable cost for company A = $ 750 ......................................................................... (Equation v)

All the other information remains the same.

∴ Amount charged by Company A = Setup charges + Variable charges

∴ Amount charged by Company A = 500 + 750 ............................................................... (From given information & Equation v)

∴ Amount charged by Company A = 1,250 ...................................................................... (Equation vi)

Also,

Amount charged by Company B = 200 + 30g ............................................................... (From Equation iv)

∴ Amount charged by Company B = 200 + (30 × 50) ....................................................... (Total guests = 50)

∴ Amount charged by Company B = 200 + 1,500

∴ Amount charged by Company B = 1,700 ..................................................................... (Equation vii)

Final Answer:-

∴ From Equations vi & vii, we can conclude that Company A will cost the least.

In this question, the answer is to find out with the help of the fixed cost and variable cost formulas. So let's first understand what variable and fixed costs mean and the formula to calculate costs.

Variable costs are expenses that varies in proportion to the number of goods or services produced by a company. In other words, they are costs that vary with the amount of activity. As a result, the costs rise as the volume of activities rises and fall as the volume of activities falls.**Total Variable Cost = Total Output Quantity x Variable Cost Per Unit Output.**

A fixed cost is any business expense that does not change in response to production or sales. Fixed costs are also known as indirect costs or overhead. Fixed costs cannot be changed to reduce expenses. Instead, they typically rely on an outside entity, such as a landlord or bank. Fixed costs include rent, insurance, and labor costs.**Fixed cost = Total cost of production - (No. of units produced x Variable cost per unit)**

To find the total cost,**Total cost= Fixed cost + Variable cost**

### Related Questions to study

### For how many games is the total cost of bowling equal for the two bowling establishments ?

### For how many games is the total cost of bowling equal for the two bowling establishments ?

### Solve the radical equation Check for extraneous solutions

### Solve the radical equation Check for extraneous solutions

### Solve 8X-4= 2(4X-4)

### Solve 8X-4= 2(4X-4)

### Determine whether a table shows a linear , quadratic or exponential function ?

### Determine whether a table shows a linear , quadratic or exponential function ?

### Two window washers start at the heights shown ,one is rising , other is descending . How long does it take for the two window washers to reach the same height ? Explain.

The rate at which an object move is refers as its speed. If an object has traveled far away from the initial place and how much time it takes? To be calculated using the average speed traveled by an object. The speed formula is speed = distance/time. To determine the units for speed, we must consider the units for distance and time.

There are three different ways to write the formula. They are:

• **speed = distance ÷ time**

• **distance = speed × time**

•** time = distance ÷ speed**

Here speed, distance, and time are internally linked. So, to calculate the value of among one, we require another unit.

For example, to determine the time required to complete a journey, we must know the distance and speed first.

### Two window washers start at the heights shown ,one is rising , other is descending . How long does it take for the two window washers to reach the same height ? Explain.

The rate at which an object move is refers as its speed. If an object has traveled far away from the initial place and how much time it takes? To be calculated using the average speed traveled by an object. The speed formula is speed = distance/time. To determine the units for speed, we must consider the units for distance and time.

There are three different ways to write the formula. They are:

• **speed = distance ÷ time**

• **distance = speed × time**

•** time = distance ÷ speed**

Here speed, distance, and time are internally linked. So, to calculate the value of among one, we require another unit.

For example, to determine the time required to complete a journey, we must know the distance and speed first.

### Solve : 2(y-6) = 3(y-4) -y

### Solve : 2(y-6) = 3(y-4) -y

### Solve the radical equation Check for extraneous solutions

### Solve the radical equation Check for extraneous solutions

### Solve : -3 (8+3h) = 5h+ 4

### Solve : -3 (8+3h) = 5h+ 4

### Solve : 5 (2X+6) = 8X+48

### Solve : 5 (2X+6) = 8X+48

### Solve for y where

### Solve for y where

### A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains . The equations 12 + 7.6n and 6 + 8n , where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains . How many smaller boxes equal the same amount of cereal in the larger box ?

### A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains . The equations 12 + 7.6n and 6 + 8n , where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains . How many smaller boxes equal the same amount of cereal in the larger box ?

### You are solving an equation with a variable on each side. Does the side on which you choose to isolate the variable affect the solution . Why might you choose one side over the other ?

### You are solving an equation with a variable on each side. Does the side on which you choose to isolate the variable affect the solution . Why might you choose one side over the other ?

### Solve for y where

### Solve for y where

### Isabel says that the equation x-2= -(x-2) has no solution because a number can never be equal to its opposite, Explain the error Isabel made .

### Isabel says that the equation x-2= -(x-2) has no solution because a number can never be equal to its opposite, Explain the error Isabel made .

### Tavon has a $50 gift card that loses $2 for each 30 day period it is not used . He has $40 card that loses $1.50 for each 30 day period it is not used .

Write and solve an equation for the number of 30 day periods until the value of the gift cards will be equal ?

The quantity of goods in general that will be exchanged for one unit of money is then the value of money. Money's value is defined as its purchasing power, or the amount of goods and services it can buy.

The time value of money (TVM) is the idea that a sum of money is worth more now than it will be at a later date because of the potential earnings in the interim. A sum of money in hand is more valuable than the same sum to be paid later. The time value of money is another name for the present discounted value.

### Tavon has a $50 gift card that loses $2 for each 30 day period it is not used . He has $40 card that loses $1.50 for each 30 day period it is not used .

Write and solve an equation for the number of 30 day periods until the value of the gift cards will be equal ?

The quantity of goods in general that will be exchanged for one unit of money is then the value of money. Money's value is defined as its purchasing power, or the amount of goods and services it can buy.

The time value of money (TVM) is the idea that a sum of money is worth more now than it will be at a later date because of the potential earnings in the interim. A sum of money in hand is more valuable than the same sum to be paid later. The time value of money is another name for the present discounted value.