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-/5 Points] DETAILS MY NOTES AUFQR2 3.4.026.MI.SA. ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A credit card company offers an annual \( 2 \% \) cash-back rebate on all gasoline purchases. If a family spent \( \$ 6,000 \) on gasoline purchases over the course of a year, what was the family's rebate at the end of the year? Step 1 Recall the basic percent equation, \( P B=A \), where \( P \) is the percent written as a decimal or fraction, \( B \) is the base, and \( A \) is the amount. When solving a percent problem, we must first identify the percent, the base, and the amount. The annual cash-back rebate of \( 2 \% \) on all gasoline purchases is the percent. Write this percent as a decimal by removing the percent sign and moving the decimal point two places to the left. \[ P=\square \] The family spent \( \$ 6,000 \) on gasoline purchases over the course of a year. \( \$ 6,000 \) is the - Select-- 2 . The family's rebate at the end of the year is the \( \square \) -Select-v .

Ask by Ortiz Zimmerman. in the United States
Feb 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Step 1: - Percent (P) = 2% = 0.02 - Base (B) = $6,000 - Rebate (A) = $120

Solution

Step 1 • The percent (P) is 2%. Written as a decimal, remove the percent sign and move the decimal point two places to the left:   P = 0.02 • The family spent $6,000 on gasoline purchases over the year. This $6,000 is the base (B). • The family’s rebate at the end of the year is the amount (A).

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The Deep Dive

Oh, the excitement of cashback rebates! It's like getting a little surprise gift at the end of the year for something you were already going to buy! Here, you identified the percent as \( 0.02 \) when you wrote \( 2\% \) as a decimal. The \( \$ 6,000 \) is your base, the total amount spent on gasoline, while the rebate will be the amount you’re calculating—like finding a hidden treasure in your wallet! Now let's put on our math hats: To find the family’s rebate, you simply multiply the base amount (\$6,000) by the decimal percent (0.02). Grab your calculator and get ready, because that means the rebate can be calculated as follows: \( 6,000 \times 0.02 \). This will yield the cashback amount—essentially the cherry on the sundae of your family's expenditures!

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