Here's a math riddle for you math lovers!?

Question

Lisa has a doll collection. She decides to give some of her dolls to her friends. She gives her friend Jenny 1/4 of her dolls plus 10.
Then she gives Becca 1/5 of the remaining dolls plus 10.
Finally she gives Julie 1/2 of the remaining dolls plus 10.
She has 5 dolls left.
How many dolls did Lisa have in the beginning?

Answer 1

She ends with x

Before Julie she has 2(x + 10)

Before Becca she has 5/4*(2(x + 10) + 10)

Before Jenny she has 4/3*(5/4*(2(x + 10) + 10) + 10)

x = 5

4/3*(5/4*(2(5 + 10) + 10) + 10)

= 4/3*(5/4*(2(15) + 10) + 10)

= 4/3*(5/4*(30 + 10) + 10)

= 4/3*(5/4*(40) + 10)

= 4/3*(50 + 10)

= 4/3*(60)

= 80
------------------------
Starts with 80
Gives 80/4 + 10 = 30 to Jenny leaving 50
Gives 50/5 + 10 = 20 to Becca leaving 30
Gives 30/2 + 10 = 25 to Julie leaving 5

Answer 2

Let d = # of dolls Lisa has.

Then, Jenny gets (1/4)d + 10.

Becca gets (1/5) [(1/4)d + 10] + 10

And, she has 5 dolls left. Therefore, everything calculated above, plus 5, should equal the total number of dolls.

(1/4)d + 10 + (1/5) [(1/4)d + 10] + 10 + 5 = d

Expanding the brackets,

(1/4)d + 10 + (1/20)d + 2 + 15 = d
(1/4)d + (1/20)d + 27 = d

Let's multiply everything by 20. We will get

5d + d + 540 = 20d
6d + 540 = 20d
540 = 14d, therefore

d = 540/14 = [a non-integer]

I think there's either something wrong with the question, or I made an error. Let's see what others come up with.

Answer 3

She starts with X

She gives Jenny
X/4 + 10
And she is left with X-X/4-10 =
3X/4-10
She gives Becca
1/5(3X/4-10)+10= 3X/20 + 8
And she is left with 3X/4-10 - 3X/20 - 8 =
12X/20 - 18 =
3X/5 - 18
She gives Julie 1/2(3X/5-18)+10=3X/10 + 1
and she is left with 3X/5-18-3X/10-1 = 5
6X/10 - 19 - 3X/10 = 5
3X/10 = 24
X/10 = 8
X = 80

Test
she gives Jenny 30 dolls
she is left with 50
she gives Becca 20 dolls
she is left with 30
She gives Julie 25 dolls
she has 5 dolls left!!!

Answer 4

let the NO. of dolls be x.
(x/4 +10)+(x/5+10)+(x/2+10)+5=x
x/4+x/5+x/2+35=x
5x+4x+10x+700=20x
19x+700=20x
x=700
verification:-700/4+10+700/5+10+700/2+10+5=700


175+10+140+10+350+15=700
700=700
HENCE PROVED

Answer 5

20

Answer 6

80 in the beginning
80 *.75 =60
60 - 10 =50
50 * .80 =40
40 - 10 =30
30 * .50=15
15-10=5
5 dolls left

Answer 7

80

Answer 8

y1 = (y0- y0/4 - 10)
y2= y1 - y1/5 - 10
y3 = y2 - y2/2 - 10
y3 = 5

substituting back into eq above start with last one
y3 = 5
y2 = 15*2 = 30
y1=40*5/4 = 50
y0=60*4/3 = 80
thus 80

Answer 9

VEN LISA HAS X DOLLS

JENNY=X/5+10
..........
WE GET
X=X/5 + X/2 +X/4 +35
X=19X+700/20
X=700

Answer 10

73