Question 675229
The recipe serves 8 but is needed to serve 12.  The difference is 4 servings, which is half the original serving size.  Therefore, 1 {{{1/2}}} of the recipe is needed to serve 12.
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2 {{{1/2}}} cups plus {{{(1/2)(5/2) = 5/4}}}
where 2 {{{1/2}}} is 2*2=4+1=5 so {{{5/2}}} as an improper fraction.
sugar requred is 
{{{(5/2) + (5/4) = (5/2)(2/2) + (5/4) = (10/4) + (5/4) = (15/4)}}}
where {{{15/4}}} is 3{{{3/4}}} cups of sugar
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{{{1/4}}} cups brown sugar plus {{{(1/2)(1/4) = 1/8}}}
{{{(1/4) + (1/8) = (1/4)(2/2) + (1/8) = (2/8) + (1/8) = highlight_green(3/8)}}}cups of brown sugar.
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{{{(14.50)/12 = x/20}}}
cross multiply
290 = 12x
x=290/12 ={{{highlight_green( 21.16)}}} for 20 houses