Lesson: Writing Equations

Comment on Writing Equations

How did you get the 4m+15 for Curly?
greenlight-admin's picture

I didn't get 4M+15 for Curly's age.
I got 2(M+5) for Curly's age.
I also got M+5 for Larry's age
And I got M for Moe's age
We are told that the sum of all 3 ages is 95
So, we get: M + M+5 + 2(M+5) = 95
When we simplify the left side of the equation, we get 4M+15 = 95
So, 4M+15 is a simplification of the left side of the equation (which represents the sum of all 3 men)

Hello, I have a question regarding ETS question page 262 #15:
For both a and b , I had a problem with solving the question.
Need your kind explanation on both question. Thank you

greenlight-admin's picture

You bet.

THE QUESTIONS:
A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12.
(A) What is the fixed total cost to charter the aircraft?
(B) What is the cost per person if 40 people charter the aircraft?

-----QUESTION A--------------
Let T = TOTAL price of charter
With 36 people, the price PER PERSON = T/36
With 40 people, the price PER PERSON = T/40

We're told that the price PER PERSON with 36 people is $12 greater than the price PER PERSON with 40 people.

In other words: price PER PERSON with 36 people is $12 MORE than the price PER PERSON with 40 people

Or: (price PER PERSON with 36 people) = (price PER PERSON with 40 people) + $12

Now we can write: T/36 = T/40 + 12 (solve for T)
To eliminate the fractions, multiply both sides by 360 to get: 10T = 9T + 4320
Solve: T = 4320

So, the TOTAL price of the charter = $4320

-----QUESTION B--------------
From above, we know that the TOTAL price of the charter = $4320
With 40 people, the price PER PERSON = T/40

So, the price PER PERSON = 4320/40 = $108

So, each person pays $108

Does that help?

Cheers,
Brent

Understood. Thank you

Thanks for the solution guys

wow.. I am able to track the questions that I did.. The attempted ones are coming in a different color.. Thanks a lot for this.
greenlight-admin's picture

Hi Reetika,

Glad you like the change!!

Cheers,
Brent

Official Guide to the GRE (1st or 2nd edition) page 244 question 13. I wrote the following equations:
x + y = 3000
0.08x + 0.1y = 256
This gave me an incorrect answer.

I subsequently switched the variables to get: 0.1x + 0.08y = 256
This gave me the correct answer.
I'm confused as to why would not the earlier equation work?
greenlight-admin's picture

The two systems you created should both give you the correct answer.

Think of it this way:
If we let x = amount of money that earned 8% interest,
...and we let y = amount of money that earned 10% interest
Then the first system is perfect

If we let y = amount of money that earned 8% interest,
...and we let x = amount of money that earned 10% interest
Then the second system is perfect

So, either system should have worked.
Given this, I have a feeling you made a small error while solving the first system.

If you want to post your solution for the first system, I can probably find the point where the solution went "off the rails"

Cheers,
Brent

https://gre.myprepclub.com/forum/each-of-the-576-houses-in-tenantville-is-owned-by-one-of-th-5105.html
Hello Brent i was on the right track in assigning variables on this questions till i saw this last part "matt owns 100 houses more than Angela". I tried to assign a variable and i couldn't. I checked the solution and found out they didn't even use the variable i found hard to decipher. How do i know what's necessary in a word problem question
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/each-of-the-576-houses-in-tenantville-i...

Interesting! I never realized that I never used the fact that Matt owns 100 houses more than Angela.
That said, it looks like that information was unnecessary.

It's VERY rare that a GRE question will contain superfluous information, so I wouldn't worry about it.

Cheers,
Brent

Jennifer has 60 dollars more than Brain. If she were to give Brain 1/5 of her money , Brain would have 25% less than the amout that jennifer would then have.How much money does Jennifer have
Please solve i started off with B=Brian
B+60= Jennifer
greenlight-admin's picture

http://www.urch.com/forums/gre-math/155943-help-me-question-please-proper-explanations.html

I face just one problem in this question, Why are we not subtracting 25% or 0.4% from this equation, i.e, 0.8(60+X) when Jennifer was to give Brian 1/5 of her money and Brian would have 25% less than the amount that Jennifer would then have?

Thanks for your help Brent!
greenlight-admin's picture

Question link: http://www.urch.com/forums/gre-math/155943-help-me-question-please-prope...

Subtracting 25% is the same as keeping 75%.
For example, if a toy costs $100, then a 25% off sale, means a buyer must PAY 75% of the original price.
Or we can say that a buyer must PAY 3/4 of the original price.

That's the rationale I used in my solution.

Does that help?

Cheers,
Brent

Thanks, it does help a lot. However, when I solve for this equation: x+0.2(60+x)=0.4-0.8(60+x), I get the answer wrong.

2x=0.4-60.
Where did I go wrong? I am not sure.

Thanks again for all the help!

greenlight-admin's picture

Hi Ketan,

Can you provide a more detailed, step-by-step solution?
At the moment, it's unclear to me what the 0.4 stands for.

Cheers,
Brent

Here's what I did: x+0.2(60+x)=25/100-0.8(60+x)

x+12+0.2x=0.4-48-0.8x
1.2x+12=0.4-48-0.8x
2x=0.4-48-12
2x=0.4-60

This is where I am stuck. Thanks for the assistance.
greenlight-admin's picture

What does 25/100 represent?
Also, 25/100 = 0.25 (not 0.4)

Thanks for highlighting the mistake. 25/100 represents the 25% less money which Brian would have. I now think that I should have subtracted 25/100 from- 0.8(60+x), i.e. 0.8(60+x)-25/100.
greenlight-admin's picture

You can't just subtract 25%.
You must subtract 25% OF SOMETHING.

If Joe has J dollars, and I have 25% less than Joe, then...
The amount of money I have = (Joe's money) - (25% of Joe's money)
= J - (25% of J)
= J - 0.25J
= 0.75J
-------------------------

Here's my full solution (starting with your approach)

Let x = Brian's money NOW
So, x + 60 = Jennifer's money NOW

GIVEN: Jennifer gives Brian 1/5 (20%) of her money
20% of Jennifer's money = 0.2(x + 60) = 0.2x + 12

So, at this point....
x + (0.2x + 12) = Brian's money
x + 60 - (0.2x + 12) = Jennifer's money

Simplify to get:
1.2x + 12 = Brian's money
0.8x + 48 = Jennifer's money

GIVEN: At this point, Brian has 25% less than the amount that Jennifer has.
25% of Jennifer's money = 0.25(0.8x + 48)
= 0.2x + 12

So, 25% LESS THAN Jennifer's money = 0.8x + 48 - (0.2x + 12)
= 0.6x + 36

We can write: 1.2x + 12 = 0.6x + 36
Solve: x = 40

So, Brian has $40 NOW, which means Jennifer has $100 NOW.

Does that help?

Cheers,
Brent

It is clear to me now. Thanks!

Regarding the 2nd from last practice problem in the list (https://gre.myprepclub.com/forum/a-sum-of-money-was-distributed-among-lyle-bob-and-chloe-f-12652.html#p37083). Could you please take a look at the calculations I posted on that page and tell me where I went wrong.
greenlight-admin's picture

You made a very small mistake. My response here: https://gre.myprepclub.com/forum/a-sum-of-money-was-distributed-among-ly...

Cheers,
Brent

Hello Brent!
https://m.youtube.com/watch?v=glnQsBkkEhM
Can you explain please how does he gets 28?
I find the value of M =4
Then if now he is 4 years in 12 years he will be 16
4*M=16
So
16x=32*12
x=24
greenlight-admin's picture

Question link: https://m.youtube.com/watch?v=glnQsBkkEhM

We must find the "number of years until Murray is 8 times as old as he is now"
M = 4. so Murray is NOW 4 years old.

8 x 4 = 32
So, 8 times Murray's PRESENT age equals 32.

So, we must determine the number of years until Murray is 32
Murray is NOW 4 years old.
So, he will be 32 years old in 28 years.

I a little confused about as below rules, I will be appreciated if you explain the Second one " A " option is Correct Or "B" option as a general rule to be applied?

1- The three consecutive integers :
F= first no.
F+1 = second no
F+2 = third no.

2- The 4 consecutive odd number )
A). (.....,1, 3, 5, 7, 9, 11, 13,.......)
F = first no
F+2 =second no
F+4 = third no
F+6 = forth no

B).
F+1 = first integers
F+2 = second
F+ 3 = third
F+5 = forth
F+7 = Fifth

Thanks
greenlight-admin's picture

1) With consecutive integers (e.g., 4,5,6,7,8...), each integer is ONE GREATER than the previous integer.
So, as you suggest, we get:
F = first #
F + 1 = second #
F + 2 = third #
etc.

2) With consecutive ODD integers (e.g., 5,7,9,11,13,15...), each integer is TWO GREATER than the previous integer.
So, we get:
F = first #
F + 2 = second #
F + 4 = third #
F + 6 = fourth #
etc.

We can verify this assignment by seeing what happens if we let F = some odd number.
For example, if F = 11, then we get:
F = 11 = first #
F + 2 = 11 + 2 = 13 = second #
F + 4 = 11 + 4 = 15 = third #
F + 6 = 11 + 6 = 17 = fourth #
etc.

Let's keep going.....

3) With consecutive EVEN integers (e.g., 4,6,8,10,12...), each integer is TWO GREATER than the previous integer.
So, we get:
F = first #
F + 2 = second #
F + 4 = third #
F + 6 = fourth #
etc.

Does that help?

Hi Brent,

regarding this https://gre.myprepclub.com/forum/qotd-13-at-a-club-meeting-there-are-10-more-club-members-2494.html

non-club members =n
club members =n+10
GIVEN: There are 10 more club members than non-members.
so n+n+10=c
2n+10=c
2n=c-10
n=(c-10)/2

Could you please help me with this.

Thanks

suppose total club umbers=c
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/qotd-13-at-a-club-meeting-there-are-10-...

We're told that c = number of CLUB MEMBERS at the meeting
In your solution, you have n + n + 10 = c, which means c = total number of people (MEMBERS and NON-MEMBERS) at the meeting.

I hope that helps.

Cheers,
Brent

Hi Brent,

Sorry I Didnt get you

Thanks
greenlight-admin's picture

You let n = non-club members
So, club members =n+10
GIVEN: There are 10 more club members than non-members.
So n + n + 10 = c

So, you are saying that (non-club members) + (club members) = c
However, this not what the question is telling us.

The question tells us that c = number of CLUB MEMBERS at the meeting.
You are saying that n + 10 = number of CLUB MEMBERS at the meeting.

So, you don't need to create a new variable (n) to describe anything.
You need only use the variable c.

Does that help?

https://gmatclub.com/forum/each-year-for-4-years-a-farmer-increased-the-number-of-trees-in-a-135487.html

For this problem I was able to break it down and understand what they wanted me to find. However I started at yr 1, instead of beginning at yr 0, is it usually the case that we would begin at yr 0.
What I did yr1: x, yr2: 5x/4: yr3:25x/16, yr4: 125x/64 and set the value in yr 4 to6250, but that was incorrect. When I looked at the solution I was off by 1 yr hence starting from yr 0. Hope this all makes sense. Please let me know if you need any clarification. Thanks and happy holidays!
greenlight-admin's picture

Labelling the years "year1", "year2", "year3" is ambiguous.
For example, what does it mean to say that year1 = x?
Does it mean the population was x at the BEGINNING of the first year or at the END of the first year?

The question tells us, "....there were 6250 trees in the orchard AT THE END OF a 4-year period"
In other words, after 4 years have ELAPSED, there were 6250 trees.
So, we should start at the beginning, before any years have elapsed (i.e., 0 years have elapsed), and go from there.

BTW, here's my solution: https://gmatclub.com/forum/each-year-for-4-years-a-farmer-increased-the-...

https://gmatclub.com/forum/a-survey-of-employers-found-that-during-1993-employment-costs-rose-168678.html

Hey Brent I came across this question and for some reason I am having difficulty with it. I went ahead and decided to set up equations for it: Beginning 93': SC+FB = 100
(During 93'): 1.033SC +1.033FB = 103.5
greenlight-admin's picture

Question link: https://gmatclub.com/forum/a-survey-of-employers-found-that-during-1993-...

Your equation SC + FB = 100 tells us that, at the beginning of 1993, the total EMPLOYMENT COSTS were $100

If SC increased 3% and FP increased 5.5%, then NEW SC = 1.03SC and NEW FB = 1.055FB
Likewise, since EMPLOYMENT COSTS increased 3.5%, then the NEW EMPLOYMENT COSTS = (1.035)($100)

So, our equation becomes: 1.03SC + 1.055FB = (1.035)($100)
In other words, 1.03SC + 1.055FB = 103.5

We now have the following system of equations:
1.03SC + 1.055FB = 103.5
SC + FB = 100

When we solve this, we get SC = 80 and FB = 20
20/100 = 20%
So, fringe-benefit costs represented 20% of employment costs at the beginning of 1993

Hello sir i have a issue to question u have already provided answer can u please help?

https://gre.myprepclub.com/forum/a-rectangular-game-board-is-composed-of-identical-squares-ar-3268.html

A rectangular game board is composed of identical squares arranged in a rectangular array of r rows and r + 1 columns.

Q1....What i did here was thinking that each sq was r and r +1 but i was wrong....can u please explain how to decipher this for future?

Q2....Can u please explain what the below part means like what is 1 through r like 1 to r would mean 1 till 10 if r = 10?
The r rows are numbered from 1 through r, and the r + 1 columns are numbered from 1 through r + 1. If r > 10,

Q3.....here i though only one would be in both at the intersection of 4 row and column but can u please help ?
Which of the following represents the number of squares on the board that are neither in the 4th row nor in the 7th
column?

Can u please help me here?
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/a-rectangular-game-board-is-composed-of...

I'm happy to help.

Q1: The word "square" tells us that each side has the same length.

Q2: The author of the question mentions that r > 10 in order to discourage students from simply testing cases.
So, that information is really just telling us that the rectangular game board has at least 11 rows and 12 columns.

If r = 11, then the rectangular game board:
- has a total of 11 rows, which are labelled 1, 2, 3, 4, . . . 9, 10, 11
- has a total of 12 columns, which are labelled 1, 2, 3, 4, . . . 9, 10, 11, 12

If r = 13, then the rectangular game board:
- has a total of 13 rows, which are labelled 1, 2, 3, 4, . . . 11, 12, 13
- has a total of 14 columns, which are labelled 1, 2, 3, 4, . . . 11, 12, 13, 14

And so on

Q3: "The number of squares on the board that are neither in the 4th row nor in the 7th column?"
This means we cannot include any squares in the 4th row.
It also means we cannot include any squares in the 7th column.
Keep in mind that a question asking us to exclude a single square wouldn't be very challenging.

Thank you for this i believe i do understand it the hint in Q1 was that its a rectangle with squares in it we have to see it from a rectangluar perspective and than imagine squares and remove them

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