Question

Milo 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 mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture?A. 0.5 gallon
B. 1.5 gallons
C. 2 gallons
D. 2.5 gallons

Answer 1

Answer:

B. 1.5 gallons

Step-by-step explanation:

Let x represent gallons of lime juice and y represent gallons of lemon juice.

We have been given that Milo wants to make 4 gallons of a mixture that is 50% lemon juice and 50% lime juice. We can represent this information in an equation as:

$x+y=4...(1)$

$y=4-x...(1)$  

Further, the 100% lemon juice should be added to a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon 50% lime juice mixture. We  can represent this information in an equation as:

$100\%\cdot x+20\%\cdot y=4(50\%)...(2)$

$\frac{100}{100}\cdot x+\frac{20}{100}\cdot y=4(\frac{50}{100})...(2)$

$x+0.2y=2...(2)$

Substituting equation (1) in equation (2), we will get;

$x+0.2(4-x)=2$

$x+0.8-0.2x=2\\\\0.8x+0.8=2\\\\0.8x=1.2\\\\x=\frac{1.2}{0.8}\\\\x=1.5$

Therefore, Milo should add 1.5 gallons of 100% lemon juice to a juice mixture that is 20% lemon juice and 80% lime juice.