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.

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?


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!!


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"


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://greprepclub.com/forum/each-of-the-576-houses-in-tenantville-is-o...

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.


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


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?


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.

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.


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


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?


It is clear to me now. Thanks!

Regarding the 2nd from last practice problem in the list (https://greprepclub.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://greprepclub.com/forum/a-sum-of-money-was-distributed-among-lyle-...


Hello Brent!
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
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

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

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 #

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 #

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 #

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 #

Does that help?

Hi Brent,

regarding this https://greprepclub.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

Could you please help me with this.


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

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

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.


Hi Brent,

Sorry I Didnt get you

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?


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-...


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

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