Question

I need to find how much money he invested for 5% of the account and 7%.

Answer 1

Answer:

He invested $32000 in the 5% account and $8000 in the 7% account

Explanations:

Total amount invested in both accounts = $40000

Let the amount invested in the 5% account be x

The amount invested in the 7% account = 40000 - x

Total interest = $2160

Let the interest on the 5% account be y

The interest on the 7% account = 2160 - y

time, T = 1 year

$\text{Interest = }\frac{P\times R\times T}{100}$

where P is the prinicipal, R is the rate, and T is the time

For the 5% account:

$\begin{gathered} y\text{ = }\frac{x\times5\times1}{100} \\ y\text{ = }\frac{5x}{100} \\ y\text{ = }0.05x\ldots\ldots\ldots(1) \end{gathered}$

For the 7% account:

$\begin{gathered} 2160-y=\frac{(40000-x)\times7\times1}{100} \\ 2160-y\text{ = }\frac{280000-7x}{100} \\ 2160-y\text{ = 2800 - 0.07x} \\ y\text{ = 007x-2800+2160} \\ y\text{ = 0.07x}-640\ldots\ldots..(2) \end{gathered}$

Equate (1) and (2)

0.05x = 0.07x - 640

0.07x - 0.05x = 640

0.02x = 640

x = 640/0.02

x = 32000

Amount invested in the 5% account = $32000

Amount invested in the 7% account = 40000 - x

Amount invested in the 7% account = $40000 - $32000

Amount invested in the 7% account = $8000