How much less sugar must he use to keep the same ratio of coconut to sugar?

Question

Mr. Harding is making coconut cookies. The recipe calls for 420 g of coconut and 120 g of sugar. Mr. Harding only has 336 g coconut. How much less sugar must he use to keep the same ratio of coconut to sugar?

Answer 1

The normal ratio (the recipe) calls for 120g of sugar for every 420g of coconut. You can think of this more simply as

 

120 / 420

 

By contrast, Mr. Harding needs to calculate another ratio: some amount x of sugar, that corresponds to his 336g of coconut. So this other ratio can be represented as

 

x / 336

 

He wants the other ratio to be the same as the recipe, meaning the two values are to be set equal to each other:

 

x / 336 = 120 / 420

 

Now we can solve for x by multiplying both sides by 336:

 

x = (120/420) * 336 = (2/7)*336 = 96.

 

So Mr. Harding needs to use 96g of sugar. However, the problem asks "how much less sugar must he use?"

 

So your answer is 120g (the recipe amount) minus 96g = 24g less sugar.