Question

Sugar and flour are mixed in the ratio 3:5 in a sweet recipe. In another recipe, 15 parts of flour are used. If these two ingredients in both recipes are in an equivalent ratio, how many parts of sugar should be used?

Answer 1

Answer is 9

Explanation:

Sugar and flavour ratio
3 :5

new mixture used
15 flavour units

`5xx3 =15` units

therefore to keep ratio same multiply sugar proportion with same number

`3xx3 = 9`

Answer 2

A slightly different approach.

Sugar is 9 for 15 of flour

Explanation:

Did you know you can and may write ratios in the format of a fraction. Within this context the numbers are not a fraction of the whole.

`("sugar")/("flour") ->3/5`

Let the unknown amount of sugar be `x` giving:

`("sugar")/("flour") ->3/5 -=x/15`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(3/5color(red)(xx1) -=x/15)`

`color(green)(3/5color(red)(xx3/3) =x/15)`

`color(green)(9/15=x/15)`

`x="sugar"=9`