Question

lesson practice 7.2.03
name
problems 1 - 2: when deven makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. this table shows how to make batches of different sizes.

1. is there a proportional relationship between cups of milk and tablespoons of chocolate syrup? circle one.

yes no not enough information
show or explain your thinking.

1. what is a constant of proportionality for this relationship?

problems 3 - 4: when you mix two colors of paint in equivalent ratios, the color you get is always the same.

1. complete the table so that each row makes the same color purple.
2. what is a constant of proportionality for this relationship?

problems 5 - 7: here is some information about the side lengths of two scaled copies, triangle a and triangle b.

1. complete the table to determine the missing side lengths of each triangle.
2. what is a constant of proportionality in this relationship?
3. what does that constant of proportionality tell you about the triangles?

Explanation:

1.

Step1: Calculate the ratio for each pair

For the first row of milk - chocolate syrup: $\frac{3}{2}=1.5$. For the second row: $\frac{12}{8} = 1.5$. For the third row: $\frac{\frac{3}{2}}{1}=1.5$. For the fourth row: $\frac{15}{10}=1.5$.

Step2: Check proportionality

Since the ratio of tablespoons of chocolate syrup to cups of milk is the same ($1.5$) for all pairs, there is a proportional relationship.

As calculated in the previous step, the ratio of tablespoons of chocolate syrup to cups of milk is always $1.5$. This ratio is the constant of proportionality.

The ratio of red to blue cups of paint is $\frac{6}{2}=3$.
For the second - row, if blue is $1$ cup, then red is $1\times3 = 3$ cups.
Let the missing blue for the third - row be $x$ when red is $9$ cups. Since the ratio is $3$, we have $3=\frac{9}{x}$, so $x = 3$ cups.
Let the missing red for the fourth - row be $y$ when blue is $4$ cups. Since the ratio is $3$, $y=4\times3 = 12$ cups.

Answer:

Yes

2.