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

$102,000

Step-by-step explanation:

Let her total amount invested be 'x'

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

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

Amount invested in German Bakery =
`\frac{\textup{1}}{\textup{6}}*\textup{x}`

Rate of interest at German Bakery = 12%

Total earnings = $3,400

Also,

Total earnings =
`\frac{\textup{1}}{\textup{3}}*\textup{x}*14\%` +
`\frac{\textup{1}}{\textup{6}}*\textup{x}*12\%`

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

or

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

or

$3,400 =
`\frac{\textup{1.2}}{\textup{18}}*\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