contestada

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.

Respuesta :

Let [tex]s_n[/tex] represent the amount is saving account after n weeks, and  

let [tex]c_n[/tex] represent the amount is checking account after n weeks.


so:

[tex]s_0=25\\\\s_1=25+5\\\\s_2=25+5+5\\\\s_3=25+5+5+5\\\\.\\\\.s_n=25+5n[/tex]

and 

[tex]c_0=50\\\\c_1=50+10\\\\c_2=50+10+10\\\\c_3=50+10+10+10\\\\.\\\\.c_n=50+10n[/tex]


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