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 $x$

A recipe for rhubarb cake calls for 111/41/4 cups of sugar for any 221/21/2 cups of flower. How many cups of flour are needed if the baker intends to use 33 cups of sugar?