Question

1. at a birthday party, the ratio of kids to adults was 8 to 3. if there were 32 kids at the party, how many adults were there? create a table to justify your answer.

1. a hot chocolate recipe calls for six tablespoons of sugar and four tablespoons of cocoa. maria wants an extra-large cup of hot chocolate, so she uses six tablespoons of cocoa. to keep the sugar to cocoa ratio equivalent to the one in the recipe, how much sugar should maria add? fill in the missing portions of the table below to help find the answer.

sugar 6
cocoa 4 6

reviewing your math

1. graph each of the following inequalities on the number lines given. remember to chose an open or closed circle.

(a) $x\geq6$
(b) $x>2$
(c) $x<13$
(d) $x\leq10$

Explanation:

Problem 4

Step1: Define ratio variable

Let the scaling factor be $k$. The number of kids is $8k$, adults is $3k$.

Step2: Solve for k

Given $8k=32$, so $k=\frac{32}{8}=4$.

Step3: Calculate adult count

Adults = $3k=3\times4=12$.

Step4: Create ratio table

Number of Kids	8	16	24	32

Step1: Find ratio scaling factor

Original cocoa = 4, new cocoa = 6. Scaling factor $k=\frac{6}{4}=1.5$.

Step2: Calculate new sugar amount

Original sugar = 6, new sugar = $6\times1.5=9$.

Step3: Fill the ratio table

Sugar	3	6	9

(a) Graph $x\geq6$

Use closed circle at 6, shade right.

(b) Graph $x>2$

Use open circle at 2, shade right.

(c) Graph $x<13$

Use open circle at 13, shade left.

(d) Graph $x\leq10$

Use closed circle at 10, shade left.

Answer:

12 adults

---

Problem 5