Question

lesson 5 - homework a bakery uses 5 tablespoons of sugar for every 2 cups of chocolate chips to make cookies. some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of sugar to chocolate chips. complete the table as you answer the questions. sugar (tbsp) 5 12 20 chocolate chips (cups) 2 4.8 8 4 what is the constant of proportionality?

Explanation:

Step1: Define proportionality ratio

Let \( S \) = sugar (tbsp), \( C \) = chocolate chips (cups). The ratio is \( \frac{S}{C} = \frac{5}{2} = 2.5 \), so \( S = 2.5C \) or \( C = \frac{S}{2.5} \).

Step2: Find C for S=12

Substitute \( S=12 \) into \( C = \frac{S}{2.5} \)
\( C = \frac{12}{2.5} = 4.8 \)

Step3: Find C for S=20

Substitute \( S=20 \) into \( C = \frac{S}{2.5} \)
\( C = \frac{20}{2.5} = 8 \)

Step4: Find S for C=4

Substitute \( C=4 \) into \( S = 2.5C \)
\( S = 2.5 \times 4 = 10 \)

Step5: Identify constant of proportionality

The constant is the ratio of sugar to chocolate chips: \( \frac{S}{C} = 2.5 \) or \( \frac{5}{2} \)

Answer:

Completed Table:

Sugar (tbsp)	Chocolate Chips (cups)
12	4.8
20	8
10	4

Constant of Proportionality:

\( \frac{5}{2} \) (or 2.5)