any mathematicians care to help problem solving?

Question

tara paid 1/2 of her game show winnings to the gov. for taxes

she invested 1/3 of her winnings at 14% in shop A and
invested 1/6 of her winnings at 12 % in shop b

total of investments earned in one year = 4000.

how much did she win on the game show?

Answer 1

You need to take the language of the word problem and convert it to mathematical expressions.

To as great a degree as possible, make them in the same terms. Then try to figure out how to substitute known things for unknown and figure the rest out:

- - - - -

OK, the first thing is that you say "Tara paid 1/2 of her game show winnings to the gov. for taxes. She invested 1/3 of her winnings at 14% in shop A and..."

Double-check that this really says that, and not ".. She invested 1/3 of her REMAINING winnings..." because you need to know if those taxes were paid BEFORE or AFTER the investments.

Assuming they were paid AFTER (that is, the word REMAINING was supposed to be in there):

Let W be the Winnings remaining after taxes,
let A be the amount of those remaining winnings invested in Shop A, and
let B be the amount of those remaining winnings invested in Shop B.

We know that A is 1/3 of the winnings and B is 1/6 of the winnings:

A = W/3
B = W/6

The return on the investment A is 14% (14/100ths of the investment) and the return on investment B is 12% (12/100ths of the investment), and these together totalled $4000:
14A/100 + 12B/100 = $4000

We can express both A and B in terms of W from the previous equations:

14(W/3)/100 + 12(W/6)/100 = $4000

Distributing to get rid of parentheses, you get:

14W/300 + 12W/600 = $4000

Converting to like terms you get:

14W/300 + 6W/300 = $4000
20W/300 = $4000

Now multiply both sides by 300 to get only terms in W to the left of the equation:

20W = 1200000

and then divide both sides of the equation by the multiplier of W, to get the value of 1W:

20W/20 = 1200000/20
W = $60000

The winnings AFTER TAXES were 60 thousand dollars -- which, since half the winnings went to taxes, means the original winnings must have been 120 thousand dollars.

Now, double-check that by plugging the numbers back in to the original givens:

"Tara paid 1/2 of her game show winnings to the gov. for taxes."

She started with $120,000 and paid $60,000 in taxes, leaving $60,000

"She invested 1/3 of her REMAINING winnings at 14% in shop A"
1/3 of $60,000 is $20,000.
14% of $20,000 is $2,800

"and she invested 1/6 of her winnings at 12 % in shop B"
1/6 of $60,000 is $10,000.
12% of $10,000 is $1,200

"total of investments earned in one year = $4000."

Does $2,800 + $1,200 = $4,000? Yes it does, so we have the right answer.

Now obviously, if the word REMAINING should not be in there, you are going to have a different answer by a factor of two -- I'll let you figure out which way that factor goes.

Answer 2

If she invested half her winnings and paid tax on the other half and the total interest in 1 year is $4000.00

it doesn't matter if you use SI or CI

A1 = A0 (1 + 14/100) - this is the interest from shop A
B1 = B0 (1 + 12/100) - this is the interest from shop B
B0 is half of A0

So you substitute and it comes out easily.

Answer number 2 is wrong. If she won $30000 then her investments would have earned $2000 only.

I get that she invested $60,000 and therefore won $120,000

Answer 3

A/3 . 14/100 + A/6. 12/100 = 4000

simplify
28A+12A=2400000

40 A=2400000

A=60 000

60 000/2= 30 000
She wins =60 000-30 000=30 000

Answer 4

she won 60000

let the amount be x
1/3 of x * 14% +1/6 of x * 12% = 4000

so , x = 60000

Answer 5

she won the same amount corrisponding to the letter grade you would get if not for the internet........

0=F