Question

When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes


cups of milk | tablespoons f cs

2 3

8 12

1 3/2

10 15



(Tablespoons of chocolate syrup)

Use the information in the table to complete the statements. Some terms are used more than once.


a. The table shows a proportional relationship between ______ and _____.

b. The scale factor shown is ______.


c. The constant of proportionally for this relationship is ______.


d. The units for the constant of proportionally are ______ per _______.

Answer 1

Answer:

Part a) The table shows a proportional relationship between tablespoons of chocolate syrup and cups of milk

Part b) The scale factor is 1.5

Part c) The constant of proportionally for this relationship is 1.5

Part d) The units for the constant of proportionality are tablespoons of chocolate syrup per cups of milk

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line

Let

x ----> the quantity of cups of milk

y ----> the quantity of tablespoons of chocolate syrup

k ---> the constant of proportionality

For y=3, x=2 -----> $k=\frac{y}{x}=\frac{3}{2}=1.5$

For y=12, x=8 -----> $k=\frac{y}{x}=\frac{12}{8}=1.5$

For y=3/2, x=1 -----> $k=\frac{y}{x}=\frac{(3/2)}{1}=1.5$

For y=15, x=10 -----> $k=\frac{y}{x}=\frac{15}{10}=1.5$

therefore

The table shows a proportional relationship between tablespoons of chocolate syrup and cups of milk

The linear equation is

$y=1.5x$

That means----> The the quantity of tablespoons of chocolate syrup is 1.5 times the quantity of cups of milk

The scale factor is equal to the ratio between tablespoons of chocolate syrup and cups of milk. Is equal to the constant of proportionality k

The scale factor is 1.5

The constant of proportionality is 1.5

The units for the constant of proportionality are tablespoons of chocolate syrup per cups of milk

$\frac{tablespoons\ of\ chocolate\ syrup}{cups\ of\ milk}$

Answer 2

The missing terms in the options generated from the given table are;

A)  i - the cups of milk used

ii - number of tablespoons of chocolate syrup used.

B) 3/2

C) 3/2

D) Teaspoons of chocolate syrup used per cups of milk used

We are given a table showing;

1) 2 cups of milk mixed with 3 tablespoons of chocolate syrup

2) 8 cups of milk mixed with 12 tablespoons of chocolate syrup

3) 1 cups of milk mixed with 3/2 tablespoons of chocolate syrup

4) 10 cups of milk mixed with 15 tablespoons of chocolate syrup

Option A; We can see the table has two columns showing the cups of milk used and the tablespoons of chocolate syrup used. Thus, the table shows a proportional relationship between the cups of milk used and the number of tablespoons of chocolate syrup used.

Option B; Scale factor is the factor of the cups of milk that yields the tablespoons of chocolate syrup.

Thus, for the first row on the table, if scale factor is x, then;

2x = 3

Thus; x = 3/2

Option C; The constant of proportionality is the scale factor which is 3/2

Option D; The units of the constant of proportionality is;

Teaspoons of chocolate syrup per cups of milk

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