Question

Sean wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice that is 30% lemon juice and 70% lime juice to make 7 gallons of the 50% lemon/50% lime juice mixture?

Answer 1

it doesn't make sens

Answer 2

did they give you the gallons of the 30%/70% mixture?

Answer 3

yes

Answer 4

not enough information

Answer 5

what do you mean

Answer 6

we need the gallons for the mixture you already have to know how much more to add, in order to get 7 gallons of final solution.

Answer 7

A. 0.5 gallon
B. 1 gallon
C. 2 gallons
D. 2.5 gallons

Answer 8

this are the answers

Answer 9

Still not enough information… What is the starting amount of the solution? If we don't know how much we start with, how can we know how much to add to? (i.e. the starting could be 1, 2, 4.5, 6, etc. gallons for all we know, since it's not specified.)

Answer 10

do you know

Applications: Systems of Linear Equations

Answer 11

for 8th grade

Answer 12

@shamil98

Answer 13

hi

Answer 14

yeah there isn't enough info to determine the 7 gallons , you need to know how many gallons the 30/70 mixture is.. the starting amount

Answer 15

any thing

Answer 16

What Sean wants: 7 gallons that's 50% lemon and 50% lime. Well, that's half and half, right?

So...what's half of 7 gallons?

Is it clear that his final mixture will include 3.5 gallons of lemon?

So...he's adding two things together. One of the things is the pure lemon juice, and the other thing is a mix. Those are my two variables. When he adds those two things together, he will have 7 gallons. L for lemon, M for mix.

L + M = 7

We know he wants 3.5 gallons of lemon. We are getting lemon from two places...from the pure lemon juice, L, and from the M. How much of the mix? 30% of the mix is lemon. So, to get 3.5 gallons of lemon, that's ALL of L, and 30%, or 0.3, of M.

L + .3M = 3.5

Those are your two equations. L + M = 7, which means he's adding some amount of the box marked "L" which includes pure lemon jucie, and some amount of the box makred "M", which is a mix. It will add up to 7 gallons. And

L + .3M = 3.5, which means he wants 3.5 gallons will be lemon juice, which is ALL of what he added from the box marked "L", plus .3 (30%) of what he added from the box marked "M".

L + .3M = 3.5

L + M = 7

Answer 17

p= # of pure lemon juice
m= # of gallons of 30/70 mixture
7= total # of gallons of 50/50 mix
p+m=7

Amount of lemon juice in p gallons of 100% lemon juice = 1p
Amount of lemon juice in m gallons of 30% lemon juice = .3m
Amount of lemon juice in 7 gallons of 50% lemon juice = 3.5
so
p+.3m=3.5

Now solve:
p+m=7
p=7-m

substitute 7-m into second equation for p
(7-m) +.3m=3.5
-.7m=-3.5
m=5

substitute 5 for m into the equation p=7-m
p=7-5
p=2 gallons of 100% lemon juice for wanted results

Figured it out, thanks to my learning coach!

Answer 18

thats an awesome solution!

Answer 19

thanks

Answer 20

You even had Shamil98 questioning the problem!

Answer 21

ya