Finding a mathematical formula for this question?

[sacred]

I solved the following question by trial method, answer is $240. However, I was unable to come out with a formula to show it. Could someone please teach me how to solve it with a mathematical formula?

"Alvin and Patrick share a sum of money in the ratio 2 : 1. If Alvin gives Patrick $60 then they will have the same amount of money. Calculate the amount of money that Alvin has at first."

Thanks in advance!

 

[stapel]

Could someone please teach me how to solve it with a mathematical formula?

We really can't teach courses within this environment. What level of math have you studied? (Middle-school pre-algebra? High-school algebra? College calculus? Something else?) Let's see if we can work with what you've already got.

"Alvin and Patrick share a sum of money in the ratio 2 : 1. If Alvin gives Patrick $60 then they will have the same amount of money. Calculate the amount of money that Alvin has at first."

When you reply with your level of study, please include a clear listing of your efforts based on that level, so we can see how to proceed. Thank you!

 

[sacred]

Hi staple,
I'm in the middle school in Malaysia with some knowledge of algebra and ratio. However, I was unable to workout with either algebra or ratio, perhaps it was due to my limited "knowledge/skill". Thanks. Hopefully this will lead us to somewhere

 

[sacred]

We really can't teach courses within this environment. What level of math have you studied? (Middle-school pre-algebra? High-school algebra? College calculus? Something else?) Let's see if we can work with what you've already got.[/FONT][/COLOR]


When you reply with your level of study, please include a clear listing of your efforts based on that level, so we can see how to proceed. Thank you!

Hi stapel,
I think i've finally figured out something by combining algebra and ratio. Thanks anyway!!

 

[ksdhart2]

My basic thought process on a problem like this starts with declaring variables. In this case, I'd let a stand for how much money Alvin gets, and p stand for how much money Patrick gets. Then, as I read through the problem I create expressions and equations to help me figure out what's going on. Here's some things you might consider:

We know that "Alvin and Patrick share a sum of money in the ratio 2:1", so this means that Alvin gets twice as much money as Patrick. What expression might you create to signify "twice as much money as Patrick?" Then, since Alvin's money and "twice as much money as Patrick" are the same amount, what equation can you create?

Next the problem tells us that "Alvin gives Patrick $60 then they will have the same amount of money." If Alvin gives Patrick $60, what new expression reflects this change? Remember that Patrick gains $60 too. So what expression reflects that change? Since these two expression you just created are also the same amount of money, what equation can you create?

Now that you have two equations, you can manipulate them and come to the correct solution.

 

[stapel]

Alvin and Patrick share a sum of money in the ratio 2 : 1. If Alvin gives Patrick $60 then they will have the same amount of money. Calculate the amount of money that Alvin has at first.

These are their situations:

original:

   +---+---+
A: |   |   |
   +---+---+

   +---+
P: |   |
   +---+


after exchange:

   +---+--+
A: |   |  |
   +---+--+

   +---+--+
P: |   |60|
   +---+--+

In the original, A[lvin] has twice as much as does Patrick. Since giving 60 to P[atrick] leaves A with an equal amount (in particular, NOT with a lesser amount), then the 60 came from A's overage.

After the exchange, A and P have the same amount. They'd had the same matching amount, with A having that amount again as his overage. He gave P 60 from his overage. Now they have the same amount, being that matching block from the original situation, plus, in P's case, the extra 60. Since A and P have the same amount, then they must BOTH have that original matching block, plus 60. So the extra portion for each of A and P must be 60.

So then how big must have A's second (original) block have been? How how much had A had to start with?