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

The sales tax is equal to
`\$2.3`

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`

Answer 2

$2.30

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`

`(\$3.80)/(\$76)=(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.