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23a. Initially, 40% of the students at the school dance are freshmen. Then, 15 more freshmen arrive, after which 52% of the students at the dance are freshmen. How many students are now at the dance after the additional freshmen arrive?

 

23b.  40 is 120% of what number?

 

23c. The school's lemonade is 10% lemon juice by volume, and the rest is sugar water. How many liters of lemon juice must be added to 20 liters of sugar water to make the school's lemonade?

 Mar 12, 2021
edited by weredumbmaster22  Mar 12, 2021
 #1
avatar+262 
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hello there Mr.CPhill i have a humble request after this question I have 2 diagram questions would you pls answer them??

 Mar 12, 2021
 #2
avatar+118069 
+2

23a

 

Let   y  be  the  total  number  at the  dance who AREN'T  freshman...let x be the number of  freshmen

 

So...initially

 

x  / ( x + y)  =    .40      cross-multiply

 

x = .40x +  .40y

 

x - .40x  =.40y

 

.60x  = .40y

 

y  = (3/2)x

 

After  15  more freshmen arrive, we  have  that

 

(x + 15)  / ( x +  (3/2)x  + 15)  =  .52

 

(x + 15) / ( 5/2 x  + 15)  = .52     cross-multiply

 

x + 15  =  .52 ( 5/2x  + 15)

 

x + 15 =  1.3x  + 7.8

 

1.3x - x  =  15 - 7.8

 

,3x  =  7.2

 

3x  = 72

 

x = 24 =  number of original freshmen

 

24(3/2)  = 36  = number not freshmen

 

Proof

 

Initially  there were  24  + (3/2)24)  = 60 students at the  dance

 

(24) / 60   = ,40  = 40%

 

After 15 more freshmen arrive.....there are  60 + 15  =  75 students

 

(24 + 15)  / ( 60 + 15)  =    39 / 75   =  .52 = 52%

 

 

cool cool cool

 Mar 12, 2021
 #3
avatar+118069 
+2

23b

 

40 =  1.2x

 

40   /1.2   = x =  100/3 = the number

 

 

23c

     L

  ______=   .10

 (L + 20)

 

L  =  .10( L+ 20)

 

L  = .10L  +  2

 

.90:L  = 2

 

L  =  2/.90   =  20/9 (litersof lemon juice)

 

cool cool cool

 Mar 12, 2021

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