Question

Malliki Williams earned a $48,000 from royalties on her cookbook.She paid a 28% income tax on these royalties. The balance wasinvested in two ways, some of it at 3.25% interest and some at1.75%. The investments produced $904.80 interest per year. Find theamount invested at each rate.

Please explain in detail

Answer 1

$20000 and $14560

Explanation:

First, we need to get the total tax paid by Malliki Williams

To get that, we have to multiply her income tax (28%) by total royalties ($48000)

28% of $48000 = $13440

Balance after tax = $48000 - $13440

Balance = $34560

She invested some of the balance ($34560) at the rate of

3.25% ---- First investment

1.75% --- Second investment

Assume her first investment is x dollars

Definitely, her second investment would be $34560 - x

3.25% of x + 1.75% (34560 - x ) = 904.8

0.0325x + 0.0175(34560-x) = 904.8 ----- Open the bracket

0.0325x + 604.8x - 0.0175x = 904.8 ------ Collect like terms

0.0325x -0.0175x =904.8 - 604.8

0.015x = 300 ------ Divide both sides by 0.015

x = 300/0.015

x = 20000

Remember that x represents her first investment

Her second investment is $34560 - $20000 =$14560