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David opens a bank account with $140 and then deposits $150 each month. Louis opens a bank account with $260 and deposits $120 each month.  How many months will it take for David and Louis to have equal amounts of money in their accounts?  A.2  B.4  C.5  D.7
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Verified Answer :

AL2006

The problem doesn't say it, but we have to assume that David and Louis both open their bank accounts at the same time, so that the number of months is the same for both of them.

-- David starts with  140  and deposits 150  each month.
After ' M ' months, he has  ( 140 + 150 M )  in his account.

-- Louis starts with  260  and deposits  120  each month.
After ' M ' months, he has  ( 260 + 120 M )  in his account.

We need to find the number of months ' M ' when both accounts
have the same amount in them.

140 + 150 M  =  260 + 120 M

Subtract  140  from each side:        150 M  =  120 + 120 M

Subtract  120M  from each side:      30 M  =  120

Divide each side by  30 :                M  =  4


Check: 
After 4 months . ..

-- David has  140 + 150M  =  140 + 150(4)  =  140 + 600  =  $740

-- Louis has  260 + 120M  =  260 + 120(4)  =  260 + 480  =  $740

-- They're equal.    yay !

For any other number of months, more than 4 or less than 4,
they're not equal.

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