Question

Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add?

Answer 1

Well, to find the answer to this, first we add the percents of pure fruit juice.
so 25% + 10% = 35%.
Then to find how much of 2 liters is 35%, first make 35% into a fraction so we can make a proportion.
so 35% becomes:
35/100.
so since 100% of the punch is 2 liters, 2 would be the denominator and since you're trying to find 35% OF 2 liters, the numerator would be represented as x so the equation would become:
35/100 = x/2
then you cross multiply so the equation becomes
100x = 35 * 2
so then you multiply 35 with 2 so the equation becomes:
100x = 70
then divide 100 on both sides so the answer would become
x = 0.7
so 35% of the 2 liters would be 1.7 liters
i hope this helped :)
if you need more help or further explanations, please ask :)

Answer 2

sorry but the 1.7 liters is not in the choices..the choices are as follows: .4 liter, .5 liter, 2 liters, 8 liters...clearly 2 and 8 liters are not the answers so I just have to focus how to get either .5 or .4... thnks by the way ^_^

Answer 3

OH WHOOPS. I DIDN'T MEAN 1.7 MY BAD, I TYPED IT WRONG, I'M SORRY.

Answer 4

well, now that you tell me the choices, i know i did it wrong, i'm sorry x_x

Answer 5

well, in the way i did it before, instead of it being 35 over 100 = x over 2, it becomes 25/100 = x/2.
so if you cross multiply and solve, it becomes 0.5 as the answer.
i'm sorry for my mistake x_x

Answer 6

you have two liters that is 10% fruit juice so you have 10% of 2 = .2 liters of fruit juice. you add say \(x\) liters of 100% fruit juice so you have
\[.2+x\] liters of fruit juice and \(2+x\) liters total that you want to 25% fruit juice. set
\[.2+x=.25(2+x)\] and solve for \(x\)

Answer 7

probably easiest to multiply by 100 to get rid of the annoying decimals and solve
\[20+100x=25(2+x)\]
\[20+100x=50+25x\]
\[75x=30\]
\[x=\frac{75}{30}=\frac{5}{2}=2.5\]

Answer 8

yey! thank you!!! so its 0.4

Answer 9

i got 0.5 o_o

Answer 10

actually i think it is 2.5, which is what i wrote

Answer 11

I actually checked it because I have the answer key, the answer is 0.4 liter....thanks guys!

Answer 12

ohh...soryr i can't really help :(

Answer 13

lol i solve upside down!

Answer 14

\[75x=30\]
\[x=\frac{30}{75}=.4\]

Answer 15

its okay, I actually solved for it using the equation you gave...