Last year, Ivan had $20,000 to invest. He invested some of it in an acount that paid 9% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $1780 in interest. How much did he invest into each account?
Milan bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $350 less than the desktop. He paid for the computers using two different finance plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $305. How much did each comupter cost before finance charges?
1200
269.3
To find out how much Ivan invested into each account, we can set up a system of equations based on the given information.
Let's assume Ivan invested $x into the account that paid 9% simple interest per year. Therefore, he invested $(20000 - x) into the account that paid 7% simple interest per year.
The interest received on the first account (9% interest rate) can be calculated as: 0.09x
The interest received on the second account (7% interest rate) can be calculated as: 0.07(20000 - x)
According to the problem, the total interest received after one year is $1780. So we can set up the equation:
0.09x + 0.07(20000 - x) = 1780
To solve this equation, we can simplify it by distributing the 0.07:
0.09x + 1400 - 0.07x = 1780
Combining like terms:
0.02x + 1400 = 1780
Next, we isolate the variable by subtracting 1400 from both sides of the equation:
0.02x = 1780 - 1400
0.02x = 380
Finally, we solve for x by dividing both sides of the equation by 0.02:
x = 380 / 0.02
x = 19000
Therefore, Ivan invested $19,000 into the account that paid 9% interest, and the remaining amount, $20000 - $19000 = $1000, into the account that paid 7% interest.
amount invested at 9% --- x
amount invested at 7% --- 20000-x
.09x + .07(20000-x) = 1780
solve for x