Suppose the local sales tax rate is 6.5 % 6.5\% and you buy a car for $ 12 , 500 \$12,500 . What is the car's total cost? Hint: Find how much tax is due first.

This problem, we're buying a car and we know that the local sales tax rate is 6.5%. The cost of the car is $12,500 So what is the total cost of the car with sales tax? And it gives us a hint. Find how much sales tax is due first. Well, we know that finding how much sales tax is due is finding our partial amount. And we already know our percent and we know our whole amount. So to find how much sales tax is due, we can set up this equation. Our partial amount X is equal to 6.5% as a decimal is 0.065 times our whole amount of $12,500 And simplifying we get x is equal to 812.5. So that's how much sales tax we would pay on a $12,500 car. So, to find our total amount for the car, we simply need to take our $12,500 and add our 812.5 and we get $13,312.50 Now there's a slightly shorter way to do this problem, and I'm going to show you that next. If we break apart our $812 here back into how we calculated it, dollars 0.065 times the cost of our car, we see that we can do some redistributing. If we pull out $12,500 we're left with one plus 0.065 in this equation, which simplifies to 25, 12,500 times 1.065. And now we can solve this problem in just one step by multiplying these two numbers together. We also get $13,312.50. This is because here, the one represents our whole value and the 0.065 represents our partial value. And so adding these two together allows us to keep that $12,500 and add on just the additional sales tax amount. And this trick will always work as long as we know we want to keep our whole amount and just add on a little bit more.

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Multiple Choice

Suppose the local sales tax rate is $6.5 percent sign$ and you buy a car for $dollar sign 12 comma 500$ . What is the car's total cost?
Hint: Find how much tax is due first.

$dollar sign 14562.5$

$dollar sign 12506.5$

$dollar sign 13312.5$

$dollar sign 14000$

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Verified step by step guidance

Identify the given values: the sales tax rate is 6.5%, and the price of the car is \$12,500.

Convert the sales tax rate from a percentage to a decimal by dividing by 100: \$6.5\% = \frac{6.5}{100} = 0.065$.

Calculate the amount of sales tax by multiplying the car price by the decimal tax rate: $\text{Tax} = 12500 \times 0.065$.

Add the sales tax amount to the original price of the car to find the total cost: $\text{Total Cost} = 12500 + \text{Tax}$.

Write the final expression for the total cost without calculating the numeric value: $\text{Total Cost} = 12500 + (12500 \times 0.065)$.

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Struggling with Beginning & Intermediate Algebra?

Suppose the local sales tax rate is 6.5%6.5\% and you buy a car for $12,500\$12,500. What is the car's total cost?Hint: Find how much tax is due first.

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Suppose the local sales tax rate is $6.5 percent sign$ and you buy a car for $dollar sign 12 comma 500$ . What is the car's total cost?
Hint: Find how much tax is due first.