Question

you begin with $25 in a savings account and $50 in the checking account. Each week you deposit $5 into savings and $10 into checking. After how many weeks is the amount in checking twice the amount in savings? write and solve an equation.

Answer 1

Let
`s_n` represent the amount is saving account after n weeks, and

let
`c_n` represent the amount is checking account after n weeks.


so:


`s_0=25\\\\s_1=25+5\\\\s_2=25+5+5\\\\s_3=25+5+5+5\\\\.\\\\.s_n=25+5n`

and


`c_0=50\\\\c_1=50+10\\\\c_2=50+10+10\\\\c_3=50+10+10+10\\\\.\\\\.c_n=50+10n`


thus to find

"the amount in checking twice the amount in savings"

we solve the equation:

50+10x=2(25+5x),

50+10x=50+10x

this is true for any x (any number of weeks)


Answer: the amount in checking is twice the amount in savings ALWAYS