Bob has two savings accounts. He deposited $200 more into account A than account B. After a period of time, account A has earned $84 in interest at 3%, and account B has earned $24 in interest at a rate of 2%.

Write an equation to represent the situation. Explain each variable used.
How much money did Bob initially deposit into each account? Solve the equation.

Question

Bob has two savings accounts. He deposited $200 more into account A than account B. After a period of time, account A has earned $84 in interest at 3%, and account B has earned $24 in interest at a rate of 2%.

Write an equation to represent the situation. Explain each variable used.
How much money did Bob initially deposit into each account? Solve the equation.

anonymous · Answer

I assume you mean Account A earned 3% annually and Account B earned 2% annually?

anonymous · Answer

yea

anonymous · Answer

OK. Let's say P is the amount Bob deposited into Account B. Then P+200 is the amount Bob deposited into Account A.
Both accounts are allowed to sit for a period of t years, but Account A makes 3% interest, and Account B only makes 2% interest. So do you know the equation for interest compounded annually? 
It's
$$A=P(1+r)^t$$
whereas A is the amount you get in total, P is your principal (your initial deposit), r is your interest rate in decimal form and t is your time in years.
So 
$$(P+200)(1+0.03)^t=P+200+84$$
$$P(1+0.02)^t=P+24$$
Now just solve this system and you will find P, the initial amount Bob deposited to account B.