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

Answer:

• 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.

$\begin{gathered} \text{ Cups of flour }:\text{ Amount of Sugar} \\ 5:2=\frac{5}{2} \\ 10:4=\frac{10}{4}=\frac{5}{2} \\ 15:6=\frac{15}{6}=\frac{5}{2} \end{gathered}$

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).

$\frac{Cups\text{ of flour}}{Amount\text{ of sugar}}\implies\frac{5}{2}=\frac{25}{x}$

Then solve the equation for x:

$\begin{gathered} 5x=25\times2 \\ x=\frac{50}{5} \\ x=10\text{ cups} \end{gathered}$

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