Question

Determine whether the pattern forms a proportion. If yes, find the amount of sugar required to prepare a cake, which uses 25 cups of flour.

Answer 1

• Yes, the pattern represents a proportion.

• 10 cups of sugar

Explanation:

To determine if the pattern forms a proportion, express as a ratio the number of cups of flour to the amount of sugar.

`\begin{gathered} \text{ Cups of flour }:\text{ Amount of Sugar} \\ 5:2=(5)/(2) \\ 10:4=(10)/(4)=(5)/(2) \\ 15:6=(15)/(6)=(5)/(2) \end{gathered}`

Since the ratios all simplify to 5/2, the pattern represents a proportion.

Therefore, for a cake that uses 25 cups of flour:

Let the amount of sugar needed = x (in cups).

`\frac{Cups\text{ of flour}}{Amount\text{ of sugar}}\implies(5)/(2)=(25)/(x)`

Then solve the equation for x:

`\begin{gathered} 5x=25*2 \\ x=(50)/(5) \\ x=10\text{ cups} \end{gathered}`

The amount of sugar required to prepare a cake, which uses 25 cups of flour is 10 cups.