A consumer recently purchased a new car and paid $48,000. This amount is $2,000 less than twice what the consumer’s friend paid for their car. Which of the following is the amount that the friend paid for their car?
A.
$23,000
B.
$46,000
C.
$25,000
D.
$50,000
The Correct Answer and Explanation is:
To solve this problem, we need to set up an algebraic equation based on the information given and solve for the unknown value.
Here’s a step-by-step explanation:
- Define the Variables: Let xxx be the amount that the friend paid for their car.
- Formulate the Relationship: According to the problem, the amount the consumer paid for the car is $48,000, which is $2,000 less than twice the amount the friend paid. We can express this relationship with the following equation:48000=2x−200048000 = 2x – 200048000=2x−2000This equation states that $48,000 is equal to $2,000 less than twice the amount the friend paid.
- Solve for xxx: To find xxx, we need to isolate it in the equation. Start by adding $2,000 to both sides of the equation:48000+2000=2×48000 + 2000 = 2×48000+2000=2x 50000=2×50000 = 2×50000=2xNext, divide both sides of the equation by 2:500002=x\frac{50000}{2} = x250000=x 25000=x25000 = x25000=xTherefore, the friend paid $25,000 for their car.
- Verify the Solution: To ensure our solution is correct, substitute x=25,000x = 25,000x=25,000 back into the original relationship to check if it holds true:Twice the amount the friend paid is 2×25000=500002 \times 25000 = 500002×25000=50000. According to the problem, the consumer paid $48,000, which is $2,000 less than this amount:50000−2000=4800050000 – 2000 = 4800050000−2000=48000This confirms that the calculated value is correct.
So, the amount that the friend paid for their car is 25000\boxed{25000}25000.