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?

weredumbmaster22 Mar 12, 2021

#1**0 **

hello there Mr.CPhill i have a humble request after this question I have 2 diagram questions would you pls answer them??

weredumbmaster22 Mar 12, 2021

#2**+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%

CPhill Mar 12, 2021