Pam has a total of $2475 in two different savings accounts.

Question

Last year, one savings account

paid 3% interest and the other account paid 6.5% interest. If she earned $116.25 in interest for
the year, how was her money divided between the two accounts?

Answer 1

Hi Josh,

 

First thing we need to do here is create some equations that represent this word problem. Let's call "x" the account that pays 3% interest, and "y" the account that pays 6.25% interest.

 

2 savings accounts that total $2475 can be represented by: X + Y = 2475

 

Next, the interest accumulated by the account X = X(0.03)

and, the intestest accumulate by the account Y = Y(0.0625)

 

Now the total interest accumulated in one year between these two accounts was $116.25 so we can add together our two equations for interest from X and Y:

0.03X + 0.0625Y = 116.25

 

Now let's solve for X:

First, rearrange the first equation so that you may put Y in terms of X:

X + Y = 2475 becomes..... Y = 2475 - X

 

Let's substitute our Y into the summated interest equation.

 

0.03X + 0.0625(2475-X) = 116.25

 

Simplifying and combining terms are as follows:

0.03X + 154.69 - 0.0625X = 116.25

 

Subtract 154.69 from both sides:

0.03X - 0.0625X = -38.44

 

-0.0325X = -38.44

 

X = 1182.77 (rounded)

 

Solving for Y:

Y = 2475 - X

Y = 2475 - 1182.77 = 1292.23

 

Lastly, we should check our work by plugging X and Y back into our original interest equation:

 

0.03(1182.77) + 0.0625(1292.23) 

35.48 + 80.77 = 116.25

 

Thus the account with 3% interest has a balance of $1182.77 and the account with 6.25% interest has a balance of $1292.23.

 

Answer 2

.03x + .065y = $116.25 (interest equation)

x + y = $2475 (total money invested equation)

 

1) Isolate a variable.

 

x = 2475 - y

 

2) Plug into the other equation.

 

.03x + .065y = $116.25

3x + 6.5y = 11625 (I'm just multiplying by 100 to get rid of the pesky decimals)

3(2475-y) + 6.5y = 11625

7425 - 3y + 6.5y = 11625

4200 = 3.5y

y=1200

 

3) Solve for x.

 

x = 2475 - 1200

x = 1275

 

4) Check your work.

 

.03(1275) + .065(1200) = $116.25 

38.25 + 78 = 116.25

116.25 = 116.25