SOLUTION: Andrew and Beatrice each have their own savings account. Beatrice’s account has $600 less than three times what Andrew’s account has. If Andrew had $300 more dollars, then he w

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Question 1208899: Andrew and Beatrice each have their own savings account. Beatrice’s account has $600 less than three times what Andrew’s account has. If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account. How much does Beatrice have?
Found 4 solutions by timofer, MathTherapy, greenestamps, math_tutor2020:
Answer by timofer(104)   (Show Source): You can put this solution on YOUR website!
Might be easier to first give variable a for Andrew's account.

Andrew, a
Beatrice, 3a-600

If the described condition, then .
(this step looks like a mistake)


Beatrice had
or she had dollars.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Andrew and Beatrice each have their own savings account. Beatrice’s account has $600 less than three times what Andrew’s account has. If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account. How much does Beatrice have?

The other person's answer is "BRUTALLY" wrong!

Let amount in Andrew's account be A
Then Beatrice's account will have 3A - 600
                    Also, 
                         2A + 600 = 3A - 600 ----- Multiplying by LCD, 2
                          2A - 3A = - 600 - 600
                              - A = - 1,200
Amount in Andrew's account, or 

Amount in Beatrice's account = 3A - 600 = 3(1,200) - 600 = 3,600 - 600 = $3,000
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Of course, there are many different ways to set up and solve this problem. Following is the way I think I would go.

"If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account."

Re-phrase that to say the amount Andrew has is $300 less than half the amount Beatrice has.

Given that....

Let 2x = the amount Beatrice has

The problem asks for the amount Beatrice has in her account. So why "2x" and not "x" for the amount she has? Because the amount Andrew has is $300 less than half what Beatrice has. Using "2x" instead of "x" eliminates the need for fractions in expressing the amount Andrew has.

Is that a "better" way to set up the problem? No, not at all. It's just what I choose to do to possibly make the ensuing algebra a bit easier.

Then, since 2x is the amount Beatrice has and the amount Andrew has is $300 less than half of that amount...

Then x-300 is the amount Andrew has

With this setup, Beatrice has 2x dollars in her account and Andrew has x-300 dollars in his. The amount Beatrice has is $600 less than three times what Andrew has:

2x = 3(x-300)-600
2x = 3x-900-600
2x = 3x-1500
x = 1500

The amount Beatrice has in her account is 2x = $3000

ANSWER: $3000
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: $3000

Explanation

a = Andrew's amount before the $300 is added later
3a-600 = Beatrice's amount

After Andrew gets an extra $300 (which I'm assuming is not from Beatrice), then the "a" becomes a+300.

Then,
Andrew's amount = (1/2)*(Beatrice's amount)
Beatrice's amount = 2*(Andrew's amount)
3a-600 = 2*(a+300)
3a-600 = 2a+600
3a-2a = 600+600
a = 1200
Andrew starts off with $1200.

Beatrice has 3a-600 = 3*1200-600 = 3600-600 = $3000

If Andrew gets that extra $300, then he'll have $1200 + $300 = $1500 which is half of the $3000 Beatrice has. This helps confirm the answer is correct.
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