Lesson: Writing Equations

Comment on Writing Equations

Hi,
how do we know that Zoe's age is 10G-13 and not 13-10G?
gmat-admin's picture

You're referring to the example at 3:00 in the video.

Let's look at some other examples.

If Joe's age is 5 years less than Ken's age (K), then to find Joe's age, we must take Ken's age and subtract 5.
We get: Joe's age = K - 5

If Joe's age is 10 years less than Ken's age (K), then to find Joe's age, we must take Ken's age and subtract 10.
We get: Joe's age = K - 10

Likewise, if Zoe's age is 13 years less than 10 time Gita's age (G), then to find Zoe's age, we must take 10 times Gita's age and subtract 13.
We get: Zoe's age = 10G - 13

Brent,
The question and the narrative are both different in the example at time 3:00. The last paragraph is stated as follows: If Zoe is 3 times as old as Liam, how old is Liam. Based on the original derivation. G = Gita's age, 2G + 5 = Liam Age, then 3(2G + 5) = Zoe. So, How come we have 10G - 13 as Zoe's age. Please, explain.
gmat-admin's picture

Great question!

Notice the question tells us TWO things about Zoe's age:

1) Zoe's age is 13 years less than 10 times Gita's age.
2) Zoe is three times as old as Liam.

These two pieces of information allow us to create an EQUATION.

From 1) we can write: Zoe's age = 10G - 13
From 2) we can write: Zoe's age = 3(2G + 5)

From these two facts, we can create the equation: 10G - 13 = 3(2G + 5)

Hi Brent for your explanation to the question on GMAT Club:
Company Q plans to make a new product next year and sell each unit of this new product at a selling price of $2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run are estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?

A. 4,200
B. 3,150
C. 2,520
D. 2,100
E. 1,800

Instead of a decimal we can keep the total selling price as a fraction so that the task becomes much easier and there's no need for estimation (according to me)
Then the equation becomes:
2x=5040+4x/5
to get 6x=25200
therefore, x=4200 (Ans. A)
Is that correct? Thanks
gmat-admin's picture

Question link: https://gmatclub.com/forum/company-q-plans-to-make-a-new-product-next-ye...

Your approach is perfectly valid - nice work.

Hi Brent,
Can you please help me with this question from OG?https://gmatclub.com/forum/a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
I tried substituting the number of bananas to get A=9- 5B/7 and substituted this in the main equation 7A+5B=63 but the calculation just gets more and more difficult after this.
Thanks in advance!
gmat-admin's picture

Quote: I tried substituting the number of bananas to get A = 9 - 5B/7 and substituted this in the main equation 7A + 5B = 63

The equations A = 9 - 5B/7 and 7A + 5B = 63 are EQUIVALENT EQUATIONS, so substituting one into the other isn't going to help.

I should mention that we can't really solve this question using regular algebra.

In high school we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the variables to POSITIVE INTEGERS, then there are times when we can find the value of a variable if we're given 1 equation with 2 variables.

ASIDE: You can see my full solution at http://www.beatthegmat.com/algebra-t297095.html

Thanks Brent! That made it much easier to understand

Hey Brent,
Sorry for bombarding you with so many questions but I really find your inputs really helpful.

For question https://gmatclub.com/forum/class-b-has-50-more-students-than-class-a-number-of-girls-in-class-a-242136.html
I found a very simple ultra easy way of solving this, so easy in fact that I almost find myself doubting the correctness. Please verify cause it practically ignores some info in the question stem.

Let there be 100 Students in Class A
Therefore 150 students in Class B

Let 'x' be the no of girls in class A = no of boys in Class B.

Therefore, the number of Boys in Class A = 100-x.
And the Boys in Class B = x

Adding the two together we get Total no of Boys
= 100-x + x= 100.

Total No of students = 150+100= 250.

Therefore, percent of boys in both the classes =
100 x 100 / 250 = 40%
Answer choice C.

Thanks, please let me know if there is any flaw in the reasoning above.
gmat-admin's picture

Very nice!!
That works perfectly, because the x's cancel out when you add (100-x) and x
it certainly makes my solution look very cumbersome :-)

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