Solving for Ingredients in a Cookie Recipe: A Mathematical Approach

One of the cornerstones of cooking, particularly baking, is getting the right measurements for your ingredients. A classic example is a cookie recipe that uses 10 times as much flour as sugar. If the total amount of these two ingredients is 8 1/4 cups, how do we determine the exact amounts of sugar and flour? Let's break it down mathematically.

Setting Up the Equation

Let's denote the amount of sugar in cups as ( s ). Given that the recipe calls for 10 times as much flour as sugar, we can represent the amount of flour as ( 10s ).

The total amount of these ingredients combined is 8 1/4 cups, which is equivalent to the improper fraction ( frac{33}{4} ) cups.

Formulating the Equation

We can now set up the equation as follows:

( s 10s frac{33}{4} )

To simplify, combine like terms:

( 11s frac{33}{4} )

Solving for Sugar

To solve for the amount of sugar ( s ), we divide both sides of the equation by 11:

( s frac{33}{4 times 11} )

( s frac{33}{44} )

( s frac{3}{4} ) cups

Calculating the Amount of Flour

Now that we have the amount of sugar, we can calculate the amount of flour:

( text{Flour} 10s 10 times frac{3}{4} frac{30}{4} )

( text{Flour} 7 frac{1}{2} ) cups

Summary of Amounts

Therefore, the recipe would require:

Sugar: ( frac{3}{4} ) cups or 0.75 cups Flour: 7 1/2 cups or 7.5 cups

Conclusion

By using algebra and a mathematical approach, we have successfully determined the exact amounts of sugar and flour needed for the cookie recipe. Understanding these proportions and calculations can be a valuable skill for anyone interested in baking or cooking.