Question

Alex purchase a plasma TV and pays 7.5% state sales tax and $45 for delivery. If Alex's total cost was $1,415.63 what was the purchase price for the TV? O $834.65 O $783.22 O $1358.73 O $1275

Answer 1

Step-by-step explanation:

1. Total cost: $1,415.63

2. Sales tax: 7.5% of the purchase price

3. Delivery fee: $45

First, let's calculate the sales tax amount:

Sales tax = (7.5/100) * Purchase price

Now, we can set up an equation to find the purchase price:

Total cost = Purchase price + Sales tax + Delivery fee

Substituting the values we have:

$1,415.63 = Purchase price + (7.5/100) * Purchase price + $45

To simplify the equation, we can combine like terms:

$1,415.63 = Purchase price * (1 + 7.5/100) + $45

Next, let's calculate the sales tax amount:

Sales tax = (7.5/100) * Purchase price

Sales tax = 0.075 * Purchase price

Now we can rewrite the equation with the sales tax amount:

$1,415.63 = Purchase price * (1 + 0.075) + $45

Simplifying further:

$1,415.63 = Purchase price * 1.075 + $45

To isolate the purchase price, we subtract $45 from both sides of the equation:

$1,415.63 - $45 = Purchase price * 1.075

$1,370.63 = Purchase price * 1.075

Finally, divide both sides of the equation by 1.075 to solve for the purchase price:

Purchase price = $1,370.63 / 1.075 ≈ $1275

Therefore, the purchase price for the TV is approximately $1275