Question: Figs and Prunes

Once we determine that F = 36, the equation 3F - 72 = F doesn't help us much. The only thing that this equation is good for is determining the value of F.

If we plug F = 36 into that equation we get: 3(36) - 72 = 36
Simplify to get: 108 - 72 = 36. As you can see, this doesn't help us determine the value of P.

That said, we COULD plug F = 36 into the equation 3F - 72 = P. This will help us determine that value of P.

When we plug in F = 36, we get: 3(36) - 72 = P
Simplify to get: 36 = P...GREAT!!

Of course, we already knew that F = P, so once we know the value of F (F = 36), we already know that P must also equal 36.

Here's one way to look at it.

Let F and P = the number of figs and prunes ORIGINALLY in the bag.

Once 24 figs are eaten, the number of figs = F-24
Since no prunes were eaten, the number of prunes = P

At this point, can we say that F-24 = P?

No, we can't say this, because there are now 3 times as many prunes as figs.
So, the number on the right is three times greater than the number on the left.

So, what can we do to make the two values equal?

Well, we can take the smaller number (F-24) and multiply it by 3.
When we do so, we can write: 3(F-24) = P

Does that help?

More here: https://www.greenlighttestprep.com/module/gre-word-problems/video/903

Looks good to me.
Alternatively, you could have also found some values that meet the given conditions.

There are half as many pears as bananas.
So, let's say there are 3 pears and 6 bananas

There are three times as many apples as pears.
Since we already said there are 3 pears, we can conclude that there must be 9 apples.

What is the ratio of the number of bananas to the number of apples?
bananas/apples = 6/9
= 2/3

Hi Birina,

It's hard to tell whether your solution is valid.
If you can show me all of the steps in your solution, I'll be able to help you.

Cheers,
Brent

You bet.

YESTERDAY
Let x = # of figs in the bag YESTERDAY
So, x = # of prunes in the bag YESTERDAY

TODAY (AFTER 24 figs are eaten)
x - 24 = # of figs in the bag TODAY
x = # of prunes in the bag TODAY

"There are now 3 times as many prunes as figs"
We can write: x = 3(x - 24)
Solve, to get: x = 36

So, there were 36 figs in the bag YESTERDAY
and there were 36 prunes in the bag YESTERDAY

After 24 figs are eaten....
There are 12 figs in the bag TODAY
There are 36 prunes in the bag TODAY
TODAY'S TOTAL = 12 + 36 = 48

Answer: B

Cheers,
Brent

Let's start by testing answer choice C (60)

If we NOW have a total of 60 prunes and figs, and there are three times as many prunes as figs, then there must be 15 figs, and 45 prunes. So, BEFORE Cherif at 24 figs, the bag contained 39 figs and 45 prunes. Since we're told the bag originally had an EQUAL NUMBER of prunes and figs, we can eliminate C.

Since answer choice C yields too many prunes, we need to start with a smaller number of figs and prunes, which means we can eliminate answers choices D and E.

Now let's test answer choice B (48)
If we NOW have a total of 48 prunes and figs, and there are three times as many prunes as figs, then there must be 12 figs, and 36 prunes. So, BEFORE Cherif at 24 figs, the bag contained 36 figs and 36 prunes. Perfect! This meets the condition that the bag originally had an EQUAL NUMBER of prunes and figs.

Answer: B