A recipe for rhubarb cake calls for #1##1/4# cups of sugar for any #2##1/2# cups of flower. How many cups of flour are needed if the baker intends to use #3# cups of sugar?

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Answer 1 · 2015-11-07T21:39:18

Taken you nearly to the end. I will let you finish it off!

The solution is a matter of ratios. Expressing ratios in fraction format for this type of problem helps and is a very powerful technique.

Consider: #("rhubarb")/("sugar") = ( 1 1/4)/(2 1/2)#

For this to work you need to look at counts. Sounds obvious but for this to work the denominators need to be the same/

#("numerator")/("denominator") -> ("count")/("size")#

Converting to quarters

#1 1/4 -> 5/4 -> color(blue)(("count")/("size")) #

#2 1/2 -> 5/2 -> 10/4->color(blue)( ("count")/("size"))#

So the ratio #( 1 1/4)/(2 1/2) -> (5/4 -: 10/4) -> 5/10-> ("sugar")/("flour")#

#color(blue)(" use counts only when size is the same")#

So #3/x = 5/10#

Inverting:

#x/3 = 10/5 =2#

You should be able to take it from this point to find #x#