Choose the correct answer.

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?

A.
0.5 gallon

B.
1 gallon

C.
2 gallons

D.
2.5 gallons

Would this be 1 gallon..?

Question

Choose the correct answer.
 
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?
 
 A.
0.5 gallon
 
 B.
1 gallon
 
 C.
2 gallons
 
 D.
2.5 gallons

Would this be 1 gallon..?

whpalmer4 · Answer

He has two kinds of juice: let's call one $s$ (for straight lemon juice) and the other $m$ (for mixture of lemon and lime).

We know that $$s+m = 7$$We also know that the amount of lemon juice in 1 unit of $s$ is 1, or the lemon juice content of $s$ is simply $1s$.  The amount of lemon juice in 1 unit of $m$ is $0.3m$.

In the final mixture, we are going to have 0.5*7 = 3.5 units of lemon juice.

$$1s + 0.3m = 3.5$$

That gives you a system of two equations in two unknowns.  Solve for $s,m$ to get your answer.

whpalmer4 · Answer

$s$ will be the amount of 100% lemon juice added to the mixture to make the 50/50 lemon/lime juice mixture.

whpalmer4 · Answer

You can verify that 1 gallon is not the correct answer:

1 gallon of lemon juice + 6 gallons of mixture gives you 1 gallon of lemon juice + 0.3*6 gallons = 1+1.8 = 2.8 gallons of lemon juice in 7 gallons of mixture.  That isn't a 50/50 blend, clearly.

praxer · Answer

x= amount of pure lemon juice
y= amount  of gallons of 30/70 mixture
7= total amount  of gallons of 50/50 mix
x+y=7

Amount of lemon juice in p gallons of 100% lemon juice = 1x
Amount of lemon juice in m gallons of 30% lemon juice = .3y
Amount of lemon juice in 7 gallons of 50% lemon juice = 3.5
so
x+.3y=3.5

Now solve:
x+y=7
x=7-y

substitute 7-y into second equation for x
(7-y) +.3y=3.5
-.7y=-3.5
y=5

substitute 5 for y into the equation x=7-y
x=7-5
x=2 gallons of 100% lemon juice

I think so,

praxer · Answer

answer must be 2 gallons. If I am not wrong.

anonymous · Answer

I think that might be right

whpalmer4 · Answer

Let's check:

2 gallons of 100% lemon juice added to 5 gallons of 30/70 mixture gives us 2 + 0.3*5 = 2+1.5 = 3.5 gallons of lemon juice and 0.7*5 = 3.5 gallons of lime juice, which is a 50/50 mixture, as desired.