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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

Arithmetic / Algebra

by phoenix9801 » Sun Jun 27, 2010 12:09 am

Hi, can someone please help to explain the step-by-step instructions (in detail) in the most simplest way and clear to understand.

1-
The total cost for company x to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is.

2-
The present ratio of students to teachers at a certain school is 20 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

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Source: Beat The GMAT — Problem Solving | Sun Jun 27, 2010 12:09 am

albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 am; Location: Bangalore, India; Thanked: 116 times; Followed by:10 members; GMAT Score:770

by albatross86 » Sun Jun 27, 2010 1:21 am

Question 1

Total cost = 10,000 + 3*20,000 = 70,000

Selling price = 8*20,000 = 160,000

Profit = Sales - Cost = 160,000 - 70,000 = 90,000

Remember to add the 10,000 but to not multiply that by number of tools because this is just a fixed cost. You should only multiply 3$ per tool with 20,000.

Question 2

S:T = 20:1
So lets say there are 20x students and x teachers Total = 20+x

Now we are adding 50 students and reducing 5 teachers.

This means we have 20x + 50 students and x - 5 teachers.

New ratio = (20x + 50) / (x - 5) = 25 / 1

=> 20x + 50 = 25x - 125
=> 5x = 175
=> x = 35

Therefore the present number of teachers = x = 35

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phoenix9801: Master | Next Rank: 500 Posts; Posts: 190; Joined: Thu Jan 14, 2010 8:29 pm; Thanked: 2 times

by phoenix9801 » Sun Jun 27, 2010 2:16 am

albatross86 wrote:Question 1

Total cost = 10,000 + 3*20,000 = 70,000

Selling price = 8*20,000 = 160,000

Profit = Sales - Cost = 160,000 - 70,000 = 90,000

Remember to add the 10,000 but to not multiply that by number of tools because this is just a fixed cost. You should only multiply 3$ per tool with 20,000.

Question 2

S:T = 20:1
So lets say there are 20x students and x teachers Total = 20+x

Now we are adding 50 students and reducing 5 teachers.

This means we have 20x + 50 students and x - 5 teachers.

New ratio = (20x + 50) / (x - 5) = 25 / 1

=> 20x + 50 = 25x - 125
=> 5x = 175

Therefore the present number of teachers = x = 35

=> x = 35

On Question 2: I really do not understand why are you reducing (x-5), and how did you get 20x, I though it was x=15

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 am; Location: Bangalore, India; Thanked: 116 times; Followed by:10 members; GMAT Score:770

by albatross86 » Sun Jun 27, 2010 2:24 am

Hi,

Sorry I reduced 5 instead of adding 5 because I misread the question.

What I meant is if there were "x" teachers, there must have been "20x" students so that the ratio is 20:1

There used to be 20x students, but now we are adding 50 more, so we have 20x + 50 students

There used to be x teachers, but now we are adding 5, so it should be x+5

So (20x+50) / (x+5) = 25/1
=> 20x + 50 = 25x + 125
5x = 75

x= 15 You are absolutely right

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 am; Thanked: 46 times; Followed by:3 members

by outreach » Sun Jun 27, 2010 2:48 am

1
total=20,000
C.P=$10,000+(3*20,000)=$70,000
S.P=(20,000*8)=$160,000
Profit=s.p-c.p=$90,000

Gross profit/tool=90,000/20,000=$4.5

2
s-students
t-teachers
s/t=20/1=>s=20t -(1)

(s+50)/(t+5)=25/1
s+50=25t+125
sub vaue of s from (1)
20t+50=25t+125
5t=75
t=15

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albatross86: Master | Next Rank: 500 Posts; Posts: 392; Joined: Sun May 16, 2010 2:42 am; Location: Bangalore, India; Thanked: 116 times; Followed by:10 members; GMAT Score:770

by albatross86 » Thu Jul 08, 2010 11:03 am

Lol this is hilarious!

The original question is students:teachers = 30:1

Here, being incorrectly written as 20:1 solving the equation 20x + 50 = 25x + 125 gives -15 not +15, but I guess we all jumped to the answer

~Abhay

Believe those who are seeking the truth. Doubt those who find it. -- Andre Gide

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Fri Jul 09, 2010 1:57 am

phoenix9801 wrote:Hi, can someone please help to explain the step-by-step instructions (in detail) in the most simplest way and clear to understand.

1-
The total cost for company x to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is.

20,000 tools produced
total production cost=10,000+3*20,000 as (to produce a batch of tools is $10,000 plus $3 per tool)
so total production cost=70,000
selling price of tools=8*20,000=1,60,000
gross profit on selling 20,000 tools=1,60,000 - 70,000=90,000
gross profit on selling 1 tool=90,000/20,000=4.5 ans

2-
The present ratio of students to teachers at a certain school is 20 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

let number of teacher be x ,so number of student=20 x
now student increased by 50 so now student number stand at 20x+50
teacher x+5
student:teacher=25:1
so we can say (20x+50)/(x+5)=(25/1)
20x+50=25x+125
solving this you will get x as -15 and that will be numbe of teacher

Ideation without execution is delusion

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matces: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Nov 29, 2012 6:18 am

by matces » Sat Dec 22, 2012 3:51 am

Is it possible to solve it like this?

8x - 10.000 - 3x

Bring it all to unit form

8x - (10.000/20.000/x) - 3x

8x - .5x - 3x = 4.5x

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed May 20, 2015 3:09 pm

phoenix9801 wrote:Hi, can someone please help to explain the step-by-step instructions (in detail) in the most simplest way and clear to understand.

1-
The total cost for company x to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is.

2-
The present ratio of students to teachers at a certain school is 20 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is

(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

Solution:

The problem first asks us to calculate the gross profit. The profit equation is as follows:

Profit = Revenue - Cost

In this particular case, we are given VARIABLE REVENUE and VARIABLE COST. This means that Company X makes a certain amount of revenue PER TOOL and has a certain cost PER TOOL. We also are given a FIXED COST. This is a cost that is constant and will not change. Thus we need to take into account the quantity of tools being produced and sold as well as the fixed cost. We can now generate a more detailed profit equation:

Profit = (number of tools sold)(revenue per tool) - [fixed cost + (number of tools made)(cost per tool)]

We are given the following:

fixed cost = $10,000

cost per tool = $3

revenue per tool = $8

Number of tools produced and sold = 20,000

We can now plug all this into our profit equation:

Profit = (number of tools sold)(revenue per tool) - [fixed cost + (number of tools made)(cost per tool)]

P = 20,000 x 8 - [10,000 + (3 x 20,000)]

P = 20,000 x 8 - [10,000 + (3 x 20,000)]

P = 160,000 - [10,000 + 60,000]

P = 160,000 - 70,000

P = 90,000

We have a profit of $90,000 for selling 20,000 tools, but remember that we need to determine the profit PER TOOL. To calculate this, we divide the total profit of $90,000 by the number of tools produced, which is 20,000. We have:

$90,000/20,000 = $9/2 = $4.50

The answer is C

Jeffrey Miller
Head of GMAT Instruction
[email protected]