Question

Tara paid​ one-half of her​ game-show winnings to the government for taxes. She invested​ one-third of her winnings in​ Jeff''s copy shop at 14​% interest and​ one-sixth of her winnings in​ Kaiser's German Bakery at 12​% interest. If she earned a total of ​$3 comma 400 on the investments in one​ year, then how much did she win on the game​ show?

Answer 1

Answer:

$102,000

Explanation:

Let her total amount invested be  'x'

Amount invested in  Jeff''s copy shop = $\frac{\textup{1}}{\textup{3}}\times\textup{x}$

Rate of interest at Jeff's copy shop = 14%

Amount invested in  German Bakery = $\frac{\textup{1}}{\textup{6}}\times\textup{x}$

Rate of interest at German Bakery = 12%

Total earnings = $3,400

Also,

Total earnings = $\frac{\textup{1}}{\textup{3}}\times\textup{x}\times14\%$  + $\frac{\textup{1}}{\textup{6}}\times\textup{x}\times12\%$  

$3,400 =$\frac{\textup{0.14}}{\textup{3}}\times\textup{x}+\frac{\textup{0.12}}{\textup{6}}\times\textup{x}$

or

$3,400 = $\frac{\textup{0.84 + 0.36}}{\textup{3}\times{\textup{6}}}\times\textup{x}$

or

$3,400 = $\frac{\textup{1.2}}{\textup{18}}\times\textup{x}$

or

x = $51,000

Now,

x is half the amount actually won as half is paid to government as tax

thus,

Actual earning = 2 × $51,000 = $102,000