Question

The amount of sales tax varies directly with the cost of the purchase. If the sales tax is $3.80 on a purchase of $76 what would be the sales tax on a purchase of $46

Answer 1

Answer:

$2.30

Step-by-step explanation:

We have been given that the amount of sales tax varies directly with the cost of the purchase.

We know that a direct variation in in form $y=kx$, where, y varies directly with x and k is constant of variation.

First of all, we will find constant of variation as:

$\text{Sales tax}=k*\text{Cost of purchase}$

$\ 3.80=k*\ 76$

$\frac{\ 3.80}{\ 76}=\frac{k*\ 76}{\ 76}$

$0.05=k$

To find the amount of sales tax on a purchase of $46, we will substitute $k=0.05$ in our equation as:

$\text{Sales tax}=0.05*\ 46$

$\text{Sales tax}=\ 2.30$

Therefore, the sales tax would be $2.30.

Answer 2

Answer:

The sales tax is equal to $\ 2.3$

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 $y=kx$

Let

y-----> the cost of the purchase

x ----> the sales tax

step 1

Find the value of k

For $y=76, x=3.80$

substitute

$k=y/x$

$k=76/3.8$

$k=20$

The linear equation is equal to

$y=20x$

step 2

what would be the sales tax on a purchase of $46

For $y=46, x=?$

substitute in the equation

$46=20x$

$x=46/20$

$x=\ 2.3$