Homework help--please!!

[dwdreamer]

Can anyone help me figure this out?
"Mary has $50.00. She goes to the mall and buys lipstick and then she buys shampoo, which is half the price of the lipstick. She then spends half of what she has left on a purse, leaving her with $15.00.
How much did the shampoo cost? How much did the lipstick cost?"

By my thinking the purse must have cost $15 if she spent half of what was left. She spent a total of $35, so that leaves $20 for the lipstick and shampoo, and that isn't working out right!! What am I doing wrong??

 

[allyphoe]

50 - lipstick - shampoo - purse = 15

shampoo = 1/2 lipstick or 2 shampoo = lipstick

.5(50 - lipstick - shampoo) = purse

substituting gets us:

50 - 2 shampoo - shampoo - (.5(50 - 2 shampoo - 1 shampoo) = 15
50 - 3 shampoo - (25 - 1.5 shampoo) = 15
50 - 3 shampoo - 25 + 1.5 shampoo = 15
25 - 1.5 shampoo = 15
1.5 shampoo = 10

Shampoo = 6.67 (6 2/3)
Lipstick = 13.33 (13 1/3)
Purse = 15
Total spent = 35
Left = 15

 

[tasha99]

Can anyone help me figure this out?
"Mary has $50.00. She goes to the mall and buys lipstick and then she buys shampoo, which is half the price of the lipstick. She then spends half of what she has left on a purse, leaving her with $15.00.
How much did the shampoo cost? How much did the lipstick cost?"

By my thinking the purse must have cost $15 if she spent half of what was left. She spent a total of $35, so that leaves $20 for the lipstick and shampoo, and that isn't working out right!! What am I doing wrong??

Hmm. . . I'm getting

$6.67 for the shampoo
$13.33 for the lipstick
$15 for the purse
$15 left over

50=15+15+2x+x
20=3x
6.67 = x (rounded cost of the shampoo)

 

[glesgalass]

50 - lipstick - shampoo - purse = 15

shampoo = 1/2 lipstick or 2 shampoo = lipstick

.5(50 - lipstick - shampoo) = purse

substituting gets us:

50 - 2 shampoo - shampoo - (.5(50 - 2 shampoo - 1 shampoo) = 15
50 - 3 shampoo - (25 - 1.5 shampoo) = 15
50 - 3 shampoo - 25 + 1.5 shampoo = 15
25 - 1.5 shampoo = 15
1.5 shampoo = 10

Shampoo = 6.67 (6 2/3)
Lipstick = 13.33 (13 1/3)
Purse = 15
Total spent = 35
Left = 15

I got the same, but that way is way too complicated for me!

15 X 2 = 30 (change and purse)

50 - 30 = 20 (spent on shampoo and lipstick)

20 ~ 3 = 6.33

lipstick is 2 x 6.33 and shampoo is 6.33.

 

[SLK1]

This is why I use credit cards...

 

[glesgalass]

This is why I use credit cards...

 

[dwdreamer]

Thanks for the help! Thats what I thought the answer was, but thought it was wrong because of the rounding.