Question

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?

Answer 1

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

Explanation:

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`