a store sells two different brands of lemonade mix. for brand a 1/2 cup if mix makes a pitcher. for brand b 1/4 cup of mix makes a pitcher. the container for brand a contains 4 more cups of mix than the container for brand b. both containers make the same number of pitchers of lemonade. how many pitchers of lemonade can each container make?

Respuesta :

Answer:

The number of pitchers produced by each container = 16 .

Step-by-step explanation:

Given,

  • Brand A requires [tex]\frac{1}{2}[/tex] cup of a mix for a pitcher
  • Brand B requires [tex]\frac{1}{4}[/tex] cup of a mix for a pitcher
  • Both containers produce the same number of pitchers
  • 2 Containers :
  1. Brand A : contains four more cups of mix than Brand B
  2. Brand B : contains [tex]x[/tex] cups of mix

⇒∴ The number of cups of mix in brand A = [tex]x+4[/tex];

  • Number of pitchers = [tex]\frac{TOTAL.NO.OF.MIX}{NO.OF.MIX.FOR.ONE }[/tex]

Number of pitchers produced by the containers :

  • Brand A : [tex]=\frac{x+4}{\frac{1}{2} } \\=2*(x+4)\\=2x+8[/tex]
  • Brand B : [tex]=\frac{x}{\frac{1}{4} }\\=4*x\\=4x[/tex]

Since both are equal:

⇒[tex]2x+8 = 4x\\8=2x\\x=4[/tex]

Thus the number of cups of mix in Brand B = [tex]x=4[/tex];

The number of pitchers produced by each container :

= [tex]\frac{4}{\frac{1}{4} } \\= 4*4\\=16[/tex]

∴The number of pitchers produced by each container = 16.

Answer:

The number of pitchers produced by each container = 16.