I need help with a college algebra word problem

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 $4000 on the investment in one year, then how much did she win on the game show?

Answer 1

Let X = amount won on game show  

 

Then amount invested at 14% is (1/3)*X  

 and  amount invested at 12% is (1/6)*X  

 

Total interest of $4000 is equal to  

 

0.14*(1/3)*X + 0.12*(1/6)*X = 4000

 

Multiply both sides by 6 to clear fractions  

 

0.14*2*X + 0.12*X = 24000

0.40*X = 24000

X = 24000/0.40 = $60000

 

Check:  1/3 of $60000 is $20000, 1/6 of $60000 is $10000, and  

            0.14*20000 + 0.12*10000 = 2800 + 1200 = $4000