can you help me with my math again?

Question

Traci spent 1/5 of her money on a T-shirt. She bought a hat that cost ¼ of the money she had left. The next day, Traci bought a bracelet that cost her 1/3 of her remaining funds. On the last day of her trip, she bought a sweatshirt that cost her ½ of the remaining money she had. She went home with $12. How much did Traci begin with on her trip? Which item cost the most money?

Answer 1

Home with 12
Sweatshirt = $12 $24 in hand 24/2
Bracelet = $12 $36 in hand 36/3
Hat = $12 $48 in hand 48/4
T-Shirt = $12 $60 in hand 60/5

all cost the same!

Answer 2

Since the only proven number you have to work with is the final amount you need to start there and go backwards to the original amount.

$12 was half of the money so she had $24 before the sweatshirt.
The sweatshirt cost $12.

Before the sweatshirt she had $24.

She bought a bracelet that cost 1/3 of what she had so the money after the bracelet is 2/3 of what she had before.

3/3 minus 1/3 equals 2/3.
$24 is 2/3 of what? 36.

so she spent $12 dollars on the bracelet.

At that point she had $36. Before that she spent 1/4 her money on a hat.
4/4 minus 1/4 leaves 3/4.
$36 is 3/4 of what she had before the hat. Add $12 to that and you have $48. Her first purchase was for 1/5 of her beginning amount.5/5 minus 1/5 equals 4/5.
So the $48 is 4/5 of the beginning amount.
Therefore the starting amount would have been $60.

with just numbers;

12 = 1/2 of ? 12 + 12 = 24

24 = 2/3 of ? since the 24 is 2 of 3 parts you divide the 24 by 2 to learn what one part equals.
24 divided by 2 = 12.
12 is 1 of the 3 parts of the number you are trying to learn.
3 of the parts now would be found by 12 x 3 = 36

36=3/4 of what? Since 36 is 3 of the parts divide 36 by 3 to learn what one part is.
36 divided by 3=12.
One part = 12. there are 4 parts so 12 x 4= 48

48 is 4/5 of the original amount
divide 48 by the number 4 to learn the value of one part.

48 divided by 4 = 12
5 x 12 = 60

Hope that helps you understand the solution...

Answer 3

Work backwards.
She ended up with $12 right before that she spent half of her money, so she spent 12 dollars on the sweatshirt. So before she bought her sweatshirt she had 24 dollars and so on.

Answer 4

Traci began with $60.
1/5 = $12
5/5 = $60

All cost the same.

Answer 5

she began with $60...most expensive item is nun becuz all 4 items she bought cost $12 each

Answer 6

tshirt: 1/5
hat: (1/4)(4/5)=1/5
bracelot: (1/3)(1-(1/4)(4/5)-1/5)=(1/3)(1-2/5)=(1/3)(3/5)=1/5
s-shirt: (1/2)(1-1/5-1/5-1/5)=(1/2)(2/5)=1/5
she spent (1/5)*4=4/5 so she had 1/5 remaining.
(1/5)x=$12
x=$60 is what she started with.