Answer:
The sales tax is equal to [tex]\$2.3[/tex]
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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
Let
y-----> the cost of the purchase
x ----> the sales tax
step 1
Find the value of k
For [tex]y=76, x=3.80[/tex]
substitute
[tex]k=y/x[/tex]
[tex]k=76/3.8[/tex]
[tex]k=20[/tex]
The linear equation is equal to
[tex]y=20x[/tex]
step 2
what would be the sales tax on a purchase of $46
For [tex]y=46, x=?[/tex]
substitute in the equation
[tex]46=20x[/tex]
[tex]x=46/20[/tex]
[tex]x=\$2.3[/tex]
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 [tex]y=kx[/tex], where, y varies directly with x and k is constant of variation.
First of all, we will find constant of variation as:
[tex]\text{Sales tax}=k*\text{Cost of purchase}[/tex]
[tex]\$3.80=k*\$76[/tex]
[tex]\frac{\$3.80}{\$76}=\frac{k*\$76}{\$76}[/tex]
[tex]0.05=k[/tex]
To find the amount of sales tax on a purchase of $46, we will substitute [tex]k=0.05[/tex] in our equation as:
[tex]\text{Sales tax}=0.05*\$46[/tex]
[tex]\text{Sales tax}=\$2.30[/tex]
Therefore, the sales tax would be $2.30.
