+589 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?
+589 hello there Mr.CPhill i have a humble request after this question I have 2 diagram questions would you pls answer them??
+128407 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%
