MHB How much money does Lucy have?

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The discussion revolves around solving a mathematical problem to determine how much money Lucy has. Participants establish that Lucy's initial amount, \(L\), is half of Mel's initial amount, \(M\), leading to the equation \(L = \frac{1}{2}M\). After both receive an additional $20, the relationship changes to \(L + 20 = \frac{3}{5}(M + 20)\). The conversation highlights the challenge of reaching the conclusion that Lucy has $60, with one participant eventually solving the problem. The thread concludes with the original poster confirming they have resolved the issue.
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What I did is:

L/2 +20 = 3/5M

L/2+20=6/5L+20

5L+200=12L+200(after putting all of them to common denominator)

I got stuck here
 

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Yazan975 said:
- - - Updated - - -

What I did is:

L/2 +20 = 3/5M

L/2+20=6/5L+20

5L+200=12L+200(after putting all of them to common denominator)

I got stuck here

I would let \(L\) be the amount of money Lucy had initially and \(M\) be the amount of money Mel had initially. From the information given about their initial amounts, we may state:

$$L=\frac{1}{2}M\implies M=2L$$

$$L+20=\frac{3}{5}(M+20)$$

Substitute for \(M\):

$$L+20=\frac{3}{5}(2L+20)$$

Can you proceed?
 
Hi Yazan975! ;)

Originally we had L = M/2.
Then Grandma gave each an additional \$20, after which it became 3/5th.
So (L + 20) = (M + 20) x 3/5.

Since the question asks for what Lucy has now, we need to find (L + 20).

EDIT: beaten to it by Mark.
 
MarkFL said:
I would let \(L\) be the amount of money Lucy had initially and \(M\) be the amount of money Mel had initially. From the information given about their initial amounts, we may state:

$$L=\frac{1}{2}M\implies M=2L$$

$$L+20=\frac{3}{5}(M+20)$$

Substitute for \(M\):

$$L+20=\frac{3}{5}(2L+20)$$

Can you proceed?

The answer sheet I have says Lucy has $60
I can't get there.
Please help

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Yazan975 said:
The answer sheet I have says Lucy has $60
I can't get there.
Please help

Nvm, thanks I got it
 
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