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A box of drinking straws is shared among Allison, Jennifer and Laura. Alisson's share is half the box of straws plus 8 straws. Jennifer's share is half the remaining number of straws plus 8 straws. Laura's share is half of the remainder plus the last 9 straws. What percentage of the drinking straws is Laura's share?

 Sep 17, 2021
 #1
avatar+35059 
+1

x = total straws

 

Al = 1/2 x + 8          leaving   1/2 x - 8

Je =   1/2 ( 1/2x-8) + 8 = 1/4x +4       leaving   1/4 x - 12

La = 1/2 ( 1/4x -12 )  + 9                    summed = x

 

 

1/2 x + 8   + 1/4x + 4     + 1/8 x +3   = x

7/8x + 15 = x

x = 120 

 

Al =  68       leaving 52

Je = 34        leaving  18 

La = 18                                       18 out of 120 = 15 % of the total

 Sep 18, 2021
 #2
avatar+282 
0

Let total straw be \(x\)
 

 

 

 

Alisson's share = \( {x\over 2}{}{}+8\)
Remaining = \(x - \)\(( {x \over 2} + 8) = {x \over 2} -8\)
Jennifer's share = \( ({x \over 4} - 4) + 8 = {x \over 4} + 4\)
Remaining = \(( {x \over 2} + 8) - ({x \over 4} + 4) = {x \over 4} - 12\)
Laura's share = \(({x \over 8} - 6) +\)Remaining

Remaining = \( ({120 \over 8}- 6) + 9 = 18\)
x% of 120 = 18 ⇒ \(x = 15\)
Laura's share = 15%

 Sep 19, 2021
edited by apsiganocj  Sep 19, 2021

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