Question

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 Nancy’s account to have TWICE as much money as Fred’s account?

(Explain your thinking)

Answer 1

it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account

Explanation:

Fred brown and his sister, Nancy, each have $15 in the bank

Initially both Fred and Nancy have $15

Every week Nancy plans to add $3 to her account

Let 'n' be the number of weeks she plans to add in her account

for 1 week, $3

For n weeks , its 3n

So amount of money in Nancy's account after 'n' weeks = 15 + 3n

Fret plans to add $1 to his account each week

for 1 week, $1

For n weeks , its 1n

So amount of money in Fred's account after 'n' weeks = 15 + 1n

Now we need to find out 'n' when

Nancy's account = 2 times of Fred's account

15 + 3n = 2(15+1n)

Distribute 2 inside the parenthesis

15 + 3n = 30 + 2n

Subtract 2n on both sides

15 + n = 30

Subtract 15 on both sides

n = 15

Hence, it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account