Linda Gramham's Cinnamon Sugar Graham Cupcake recipe for 36 cupcakes requires 1 1/4 cups of sugar. How much sugar is required for 900 cupcakes? Reduce to lowest terms.

First, it is convenient to convert the mixed fraction corresponding to the time to improper. To do this, the integer is multiplied by the denominator, to which the numerator is added. Divide this result by the denominator. The denominator of the improper fraction will be the same as the mixed number had. In summary:

[tex]a\frac{b}{c}=\frac{c*a+b}{c}[/tex]

In this case:

[tex]1\frac{1}{4}=\frac{4*1+1}{4}[/tex]

Solving:

[tex]1\frac{1}{4}=\frac{4+1}{4}[/tex]

[tex]1\frac{1}{4}=\frac{5}{4}[/tex]

On the other side, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, where a, b and c are known and x is the value to be calculated:

a ⇒ b

c ⇒ x

So:

[tex]x=\frac{cxb}{a}[/tex]

In this case, the rule of three can be applied as follows: Linda Gramham's Cinnamon Sugar Graham Cupcake recipe for 36 cupcakes requires [tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups of sugar. If 900 cupcakes are made, how much sugar is required?

36 cupcakes ⇒ [tex]\frac{5}{4}[/tex] cups of sugar

900 cupcakes ⇒ x

Then:

x= (900 cupcakes× [tex]\frac{5}{4}[/tex] cups of sugar)÷ 36 cupcakes

Solving:

x= [tex]\frac{125}{4}[/tex] cups of sugar

In summary,[tex]\frac{125}{4}=31\frac{1}{4}[/tex] cups of sugar is required for 900 cupcakes.

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