Lesson: Introduction to Word Problems

You're referring to: http://gre.myprepclub.com/forum/gre-math-challenge-91-tina-ed-and-lauren...

We want to create a ratio for Tina's age: Ed's age: Lauren's age

If we want to do so algebraically (as you are attempting to do), we need to use the same variable for all 3 ages.

Your calculations are fine up to 6E=3T and 18L=6E. In fact, we can write: 3T = 6E = 18L, but this doesn't tell us anything about our required ratio. All you have done is eliminated the variables.

From here, one option is to find a set of values for T, E and L that satisfy your equation 3T = 6E = 18L.

One option is T = 6, E = 3 and L = 1

So, the ratio T : E : L = 6 : 3 : 1

Alternatively, if we want to express each person's age using the same variable, we might take 6E = 3T and divide both sides by 3 to get: T = 2E

Likewise, we might take 18L = 6E and divide both sides by 18 to get: L = (1/3)E

So, the ratio T : E : L = 2E: E : (1/3)E

Divide all 3 parts by E to get: T : E : L = 2 : 1 : 1/3

Multiply all 3 parts by 3 to get: T : E : L = 6 : 3 : 1

Let's use an easier example.

Let's say the number of boys is ten times the number of girls.
If B = # of boys, and G = # of girls, then we can write: 1B = 10G
Can we then eliminate the variables and conclude that the ratio of the number of boys to the number of girls 1 to 10? No.

However, if we recognize that we the number of boys = 10G, and the number of girls = G, we CAN say that the ratio of the number of boys to the number of girls 10G to G.

If we now take this ratio, and divide both parts by G, we can conclude that the ratio of the number of boys to the number of girls 10 to 1.

Notice that, in my solution, I used the SAME VARIABLE to represent both parts of the ratio.

Happy to help.

IMPORTANT: Please note that the question is meant to provide an overview of how to solve word problems.

Later, in the video at https://www.greenlighttestprep.com/module/gre-word-problems/video/909, we see the full solution to the question.

That said, let's solve the question together.

In the video solution, we determine their ages 4 YEARS FROM NOW:
Soo's age = M + 8 + 4 = M + 12
Marco's age = M + 4

We're told that, IN 4 YEARS, Soo is TWICE as old as Marco

This means the value of M + 12 is TWICE the value of M + 4
In other words M + 12 = 2 TIMES M + 4
In other words, M + 12 = 2(M + 4)

Does that help?

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/qotd-6-in-a-single-line-of-people-waiti...

There are two components to this question:
- The CURRENT situation.
- The HYPOTHETICAL situation.

The question: In a single line of people waiting to purchase tickets for a movie, there are CURRENTLY 10 people behind Shandra. IF (the word IF here sets up a HYPOTHETICAL situation) 3 of the people who are currently in line ahead of Shandra purchase tickets and leave the line, and no one else leaves the line, there WILL BE 8 people ahead of Shandra in line. How many people are in the line CURRENTLY?

So, we want to find the number of people in line BEFORE as a hypothetical situation occurs (i.e., the current situation).

Does that help?

Given: Danny has a test average (arithmetic mean) of 75 on ten 100-point tests.
Let's say Danny scored 75 out of 100 on each of the 10 tests.
So, the total number of points he scored = (10)(75) = 750

Let x = the number of additional tests Danny will take
So, the TOTAL number of tests Danny will take all together = 10 + x

Now let's say Danny scores 100 out of 100 on each of these x tests.
So, the number of points Danny scores on these x tests = 100x

So, after Danny takes the additional x tests, the total number of points = 750 + 100x

This means his average = (750 + 100x)/(10 + x)

We want the cumulative average to be greater than 90 points (out of 100)
So we get: (750 + 100x)/(10 + x) > 90
Multiply both sides of the inequality by (x + 10) to get: (750 + 100x) > (90)(10 + x)
Expand: 750 + 100x > 900 + 90x
Subtract 90x from both sides: 750 + 10x > 900 + 90x
Subtract 750 from both sides: 10x > 150
Divide both sides by x: x > 15

Since x > 15, we can be certain that x > 12

Answer: A