Question 1150810
let  the number of the small hamburger patties be {{{x}}} and the number of the large hamburger patties {{{y}}}

given:

a small hamburger patty uses {{{1/6}}} pound  of ground beef: total {{{(1/6)x}}}

a large patty uses {{{1/3}}} pound of ground beef:  total {{{(1/3)y}}}

if she wants to make {{{twice}}} as many large patties as small patties, than 

{{{y=2x}}}.....eq.1 

if she using {{{10}}} pounds of ground beef, than

 {{{(1/6)x+(1/3)y=10}}}......eq.2 


substitute {{{y}}} from eq.1


{{{(1/6)x+(1/3)2x=10}}}.............solve for {{{x}}}

{{{x/6+2x/3=10}}}.........both sides multiply by {{{6}}}

{{{x+4x=60}}}

{{{5x=60}}}

{{{x=highlight(12)}}}-> the number of the small hamburger patties 


go to {{{y=2x}}}.....eq.1 substitute {{{x}}}

{{{y=2*12}}}

{{{y=highlight(24)}}}-> the number of the large hamburger patties


check:


{{{(1/6)x+(1/3)y=10}}}......eq.2 

{{{(1/6)12+(1/3)24=10}}}

{{{2+8=10}}}

{{{10=10}}}