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Marlena and Christina their first savings account on the same day. Christina opened her account with $50 and plans to deposit $10 every month. Marlena opened her account with 30 dollars and plans to deposit $15 every month. After how many months will their two accounts have the same amount of money? What will the amount be.

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Thisisbenmanleyid
y = 10x + 50
y = 15x + 30

where y = the amount of money in their account and x = the number of months.
Because "10x+50" is equal to y, and "15x+30" is also equal to y, it must be true that "10x+50" is equal to "15x+30". Then solve for x:

[tex]10x+50=15x+30\\-5x=-20\\x=4[/tex]

Now that you have x, you can plug it in to one of the equations to find y:

[tex]y=10x+50\\y=10(4)+50\\y=40+50\\y=90[/tex]

So x = 4 and y = 90.  Therefore...

After 4 months, both accounts will have the same amount of money; $90.

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