Question

You invested $ 7000 between two accounts paying 3 % and 5 % annual? interest, respectively. If the total interest earned for the year was $ 290 comma how much was invested at each? rate?

Answer 1

Answer:

In the first account was invested $\ 3,000$  at 3%

In the second account was invested $\ 4,000$  at 5%

Step-by-step explanation:

we know that

The simple interest formula is equal to

$I=P(rt)$

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

First account

$t=1 years\\ P=\ x\\ r=0.03$

substitute in the formula above

$I=x(0.03*1)$

$I=0.03x$

Second account

$t=1 years\\ P=\ (7,000-x)\\ r=0.05$

substitute in the formula above

$I=(7,000-x)(0.05*1)$

$I=350-0.05x$

Remember that

The interest is equal to $\ 290$

so

Adds the interest of both accounts

$0.03x+350-0.05x=\ 290$

$0.05x-0.03x=350-290$

$0.02x=60$

$x=\ 3,000$

therefore

In the first account was invested $\ 3,000$  at 3%

In the second account was invested $\ 7,000-\ 3,000=\ 4,000$  at 5%