# Question: Figs and Prunes

## Comment on Figs and Prunes

### I don't understand why you

I don't understand why you can't plug in the value of F into the equation 3F-72=F?

Doesn't that equation take into account the 24 that were eaten? ### Once we determine that F = 36

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.

Can you please help me in understanding "3 times as many prunes as figs", when i try to solve the problem without looking into the solution i wrote F-24 = 3P; ### Here's one way to look at it.

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?

### Yes, indeed it helped. Thank

Yes, indeed it helped. Thank you!

### In a fruit basket, there are

In a fruit basket, there are half as many pears as bananas, and three times as many apples as pears. What is the ratio of the number of bananas to the number of apples?

solution:

2P = B
A = 3P

B/A = 2/3 ### Looks good to me.

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

### I Solved the question by

I Solved the question by creating the following equation F-24=3(F-24). And then plug in the value of f in the 3(F-24) equation. Is this this the right way to solve this question. ### Hi Birina,

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.

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