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

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

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

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%