Need help: What is the original number of green jelly beans?

[Cheery]

Jon had a container of green jelly beans and red jelly beans. If he eats 12 green jelly beans, the ratio of green jelly bean to red jelly bean will become 5:4. If he eats 12 red jelly beans, the ratio of green jelly beans to red jelly beans will then be 7:5. What is the original number of green jelly beans?

Anyone can help? Thank you!

 

[ksdhart]

I think a good first step here would be to define some variables. It works best to assign variables to amounts that are unknown or that vary. So, let's assign two variables. Let g represent the number of green jelly beans Jon has. And let r represent the number of red jelly beans Jon has. Then can you create an expression representing the total number of jelly beans Jon has? With those variables in mind, here's a few questions to hopefully get you thinking in the right direction.

The first part of the problem says that "if [Jon] eats 12 green jelly beans, the ratio of green jelly bean to red jelly bean will become 5:4." First, can you create an expression representing how many green jelly beans Jon has if he has eaten 12 of them? Next, what do you know what ratios and how they're related to fractions? And what does it mean when two ratios are said to the equal (or the same)?

Then the second part of the problem says "if [Jon] eats 12 red jelly beans, the ratio of green jelly beans to red jelly beans will then be 7:5." Apply the same process as you did for the green jelly beans to this. What do you get? And now that you've got two equations to work with, can you work out the value of g?

If you get stuck again, please include all of your steps and work, even if you know it's wrong, when you reply back. Good luck.

 

[stapel]

Jon had a container of green jelly beans and red jelly beans. If he eats 12 green jelly beans, the ratio of green jelly bean to red jelly bean will become 5:4. If he eats 12 red jelly beans, the ratio of green jelly beans to red jelly beans will then be 7:5. What is the original number of green jelly beans?

Since you've posted this to "arithmetic", I'll assume that you don't know anything about algebra, and thus that you need a middle-school (or earlier) method of solution.

Draw five squares in a row, connected (like a long rectangle, divided into five equal sub-squares) in a "bar". Label this bar as "G", for "green". Add another, smaller, box at the end, and fill this with "12", being the twelve that he'd removed.

Under this, draw another bar, but make this one only four squares long, with these squares being the same size as the previous bar's squares. Label this bar as "R", for "red". These two bars represent the total number of beans. Your drawing should look something like this:

G: *---*---*---*---*---*-*
   |   |   |   |   |   |1|
   |   |   |   |   |   |2|
   *---*---*---*---*---*-*
R: |   |   |   |   |
   |   |   |   |   |
   *---*---*---*---*

Now draw the other situation similarly. You should get something that looks like this:

G: *--*--*--*--*--*--*--*
   |  |  |  |  |  |  |  |
   |  |  |  |  |  |  |  |
   *--*--*--*--*--*--*--*
R: |  |  |  |  |  |1|
   |  |  |  |  |  |2|
   *--*--*--*--*--*-*

Look at the green beans. Since the number of beans hasn't changed (we've made Jon put all the beans back in), the five big boxes in the first drawing, plus the twelve extra, is the same number of beans as the seven small boxes in the second drawing. Can we relate these two bars?

If you draw three horizontal lines through the five big boxes in the first drawing, you'll have twenty quarter-big boxes, plus twelve beans. If you draw two horizontal lines through the seven small boxes in the second drawing, you'll have twenty-one third-small boxes. This means that you'll have twenty quarter-bigs plus twelve, which equals twenty third-smalls plus one third-small.

If you've got twenty groups plus twelve, and this equals twenty groups plus a group, what is the size of "a group"? So what is the size of one third-small box? Then what is the size of one small box? Then what is the size of seven small boxes? So how many green beans are there?

Where does this lead you?