30% = 30/100 = 0.3
4% = 4/100 = 0.04
1.5%= 1.5/100 = 0.015
After tax: $200,000 x 0.3 = $140,000 ---> This is the amount you will invest
You separated the $140,000 in two different amounts (lets call them A and B) to invest at 4% and 1.5%, respectively, giving you earnings of $4,350 each year.
Thus, A+B = $140,000
A at 4% + B at 1.5% should give you $4,350
So
(A x 0.04) + (B x 0.015) = $4,350
As we said A+B = $140,000 so you can transform that in B = $140,000 - A
Now apply the transformation:
(A x 0.04) + (B x 0.015) = $4,350
(A x 0.04) + (($140,000 - A) * 0.015)) = $4,350 ---> You just replaced the B for ($140,000 - A)
Just multiply the numbers in brackets
0.04A + $2,100 - 0.015A = $4,350 ---> remember that in here you just multiplied the $140,000 and A individually with the 0.015
0.04 A - 0.015 A = $4,350 - $2,100 ---> Separated the numbers with As in one side and regular numbers on the other side
Then to the Math
0.025A = $2,250
A = $2,250 / 0.025
A= $90,000
So you invested a total of 140,000, part A is $90,000 so part B must be ($140,000 - $90,000) $50,000.
Lets see if it is correct.
A) $90,000 * 0.04 = $3,600
B) $50,000 * 0.015= $750
Total $3,600 + $750 = $4,350.
Congrats! You have plenty of money!
Linda won $200,000 in a state lottery. She first paid income tax of 30% on the winnings. Of the rest she invested some at 1.5% and some at 4% earning $4350 interest per year. How much did she invest at each rate?
please show your work and tell me what you are doing throughout the problem
