Question

( 20 PTS HELP FAST PLEASE I DON'T UNDERSTAND HOW TO DO THIS ) Fred Brown and his sister, Nancy, each have $15 in the bank. Every week Nancy plans to add $3 to her account. Fred who loves to spend money when he has it, plans to add $1 to his account each week. How many weeks will it take for Nancy’s account to have twice as much money as Fred’s account? (Explain your thinking using words and numbers.)

Answer 1

You don't have to give me that many points. :)
OK so let's write this in equation form. First thing we think about is if the equation arithmetic (they add the same amount of money each week) or geometric (they add steadily increasing or decreasing amounts of money each week). Since Nancy and Fred add a fixed amount of $3 and $1 respectively, we're going to call them arithmetic sequences.

The equation for an arithmetic sequence is
an=a0+dn, where d is the amount of money added every week, n is the week number they're on and a0 is the amount of money they would've had a week before the first week. I'll explain this more in detail.

So Nancy increases by $3 every week: d=3. n is what we want to find. She starts out with $15. Imagine she had the same rule (increasing by $3) but started a week earlier. The term before 15 is 12. So a0 is 12. Her equation is an=12+3n. Let's do the same for Fred.

Fred increases by $1 and if he started a week earlier, he would've started with $14, so his equation is an=14+n. Now you want to find n so that Nancy's account (the first equation equals two times as much money as Fred has (the second equation.

So 12+3n=2(14+n).
Solving for n,
12+3n=28+2n
Combine like terms, so subtract 2n from both sides and then subtract 12 from both sides.
12+n=28
n=16
So on the 16th week, Nancy will have twice as much money as Fred. Hope this helped!