MATH SOLVE

7 months ago

Q:
# 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 gallonB. 1.5 gallonsC. 2 gallonsD. 2.5 gallons

Accepted Solution

A:

Answer:B. 1.5 gallonsStep-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:[tex]x+y=4...(1)[/tex][tex]y=4-x...(1)[/tex] 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:[tex]100\%\cdot x+20\%\cdot y=4(50\%)...(2)[/tex][tex]\frac{100}{100}\cdot x+\frac{20}{100}\cdot y=4(\frac{50}{100})...(2)[/tex][tex]x+0.2y=2...(2)[/tex]Substituting equation (1) in equation (2), we will get;[tex]x+0.2(4-x)=2[/tex][tex]x+0.8-0.2x=2\\\\0.8x+0.8=2\\\\0.8x=1.2\\\\x=\frac{1.2}{0.8}\\\\x=1.5[/tex]Therefore, Milo should add 1.5 gallons of 100% lemon juice to a juice mixture that is 20% lemon juice and 80% lime juice.