Question

Yesterday, two friends went into a bank to open savings accounts. Katie started by putting $2 in her account, and she will deposit an additional $5 each week. Darnel made no initial deposit, but he will add $6 more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance?

Answer 1

Week 3. Katie started by making a $2 deposit week 1. Week 2 Katie deposited $5 more to make $7 in her account. On Week 3 she deposited $5 that bought her account to $12. Darnel did not deposit anything Week 1. Week 2 he deposited $6. Week 3 he deposited $6 for a total of $12.

Answer 2

Answers:

It takes 2 weeks for the accounts to be equal

The balance will be $12 for each account

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Step-by-step explanation:

x = number of weeks

For Katie, she starts off with $2 and adds $5 per week. This means her expression is 5x+2 to represent how much money she has after x weeks.

Darnel's expression is 6x to indicate he deposits $6 per week.

Set those two expressions equal to one another and solve for x.

6x = 5x+2

6x-5x = 2

x = 2

At the 2 week mark is when the two accounts will have the same amount of money. The balance will be

Katie's balance = 5x+2 = 5*2+2 = 10+2 = 12

Darnel's balance = 6x = 6*2 = 12

Both balances will be $12 at week 2.