application of systems

Question

You split $1500.00 between 2 savings accounts.

One pays 4% and the other pays 5%.

After 1 year you have earned $69.50.

How much was in the 4% account ?

Answer 1

Hi Joy, if we let x represent the amount of money in the account that pays 4%, then 1500 - x is the amount of money in the account that pays 5%. 

 

Equation:

 

.04x + .05 * (1500 - x) = 69.50

 

I do not like to work work with decimals, so multiple each term by 100:

 

4x + 5 * (1500 - x) = 6950

 

Clear the parenthesis:

 

4x + 7500 - 5x = 6950

 

-x + 7500 = 6950

 

Subtract 7500 from both sides:

 

-x = -550

 

Multiply both sides by -1:

 

x = 550

 

Answer: you placed $550.00 in the account that pays 4%.

 

Check:

 

Subtract 550 from 1500 to find out how much was placed in the account paying 5%.

 

1500 - 550 = 950

 

$950.00 was placed in the account paying 5%.

 

.04 * 550 + .05 * 950 = 69.50

 

22.00 + 47.50 = 69.50

 

69.50 = 69.50, values check.

 

Questions?

Answer 2

If the amount invested in the 4% account is x

Then the amount invested at 5% is 1500-x

 

You have not stated whether we are using simple.

interest or compound interest so I will assume we

are using simple interest where  I = Prt ...

Interest = Principle*rate*time

 

The interest earned at 4% in 1 year is .04(x)(1) = .04x

The interest earned at 5% in 1 year is .05(1500-x)(1) = 75 - .05x

Total interest earned is the sum of those two.

 

69.5 = .04x + 75 - .05x

69.5 -75 = -.01x

x = (-5.5)/(-.01)

x = $550

 

He invested $550 at 4%

 

1500-x = 1500-550 = $950 invested at 5%

 

Hope this helps.  Good luck.