Question

For the situation below determine the independent value, the dependent value, and the constant of proportionality for both ratios. Confirm your calculations by setting up a proportion with the two ratios and then cross-multiplying.
A package of 7 steaks costs $44.10. A package of 11 steaks costs $69.30.

Answer 1

Answer:

see the explanation

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 $k=\frac{y}{x}$ or $y=kx$

Let

x ----> the number of steaks in the package

y ----> the cost

In this problem

The independent value or input value is the number of steaks (variable x)

The dependent value or output value is the cost (variable y)

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

$k=\frac{y}{x}$

First ratio

x=7, y=44.10 ---->  $k=\frac{44.10}{7}\ \ /steak$

Second ratio

x=11, y=69.30 ---->  $k=\frac{69.30}{11}\ \ /steak$

Verify the proportions

$\frac{44.10}{7}=\frac{69.30}{11}$

cross-multiplying

$44.10(11)=69.30(7)$

$485.1=485.1$  ---> is true

therefore

The relationship between the variables, x, and y, represent a proportional variation