Joe paid 14.00 for a board game this is 70% off the original price what is the original price? A. 21.00 B. 20.00
The correct answer and explanation is:
Let’s solve the problem step-by-step:
Problem:
Joe paid $14.00 for a board game, and this price reflects a 70% discount off the original price. What was the original price?
Step 1: Understand what “70% off” means
- A 70% discount means Joe paid only 30% of the original price, because 100% – 70% = 30%.
- So, the $14.00 Joe paid is 30% of the original price.
Step 2: Set up the equation
Let PP be the original price.
Since Joe paid 30% of PP, we can write:
0.30×P=140.30 \times P = 14
Step 3: Solve for PP
Divide both sides by 0.30:
P=140.30P = \frac{14}{0.30}
P=46.67P = 46.67
Step 4: Check the given choices
The calculation gives an original price of $46.67, but the options are:
- A) 21.00
- B) 20.00
Neither is close to $46.67.
Let’s re-examine the problem:
If Joe paid $14, which is 70% off, meaning he paid 30% of the price, the original price should be: Original price=Amount paidPercent paid=140.30=46.67\text{Original price} = \frac{\text{Amount paid}}{\text{Percent paid}} = \frac{14}{0.30} = 46.67
This is mathematically correct.
Conclusion:
- The original price is approximately $46.67, which is not listed in the options.
- If the problem expects one of the given answers, it might mean that the question is misphrased or that the discount is not 70% off but something else.
Alternative interpretation:
If $14 represents 70% of the original price (not a 70% discount), then: 0.70×P=140.70 \times P = 14 P=140.70=20P = \frac{14}{0.70} = 20
That matches option B) $20.00.
Final answer:
If Joe paid $14 after a 70% discount, the original price is about $46.67 (not in choices).
If Joe paid $14 which is 70% of the original price (meaning 30% off), then the original price is:
$20.00 (Option B).
Explanation (300 words):
When dealing with discounts, it’s important to understand the language carefully. The phrase “70% off” means the price is reduced by 70%, so the customer pays only 30% of the original price. If Joe paid $14 after a 70% discount, then $14 represents 30% of the original price. To find the original price, divide the paid amount by 30% (or 0.30). This calculation gives about $46.67, which means the original price was nearly $47 before the discount.
However, if the question’s options do not include this value, there might be a misunderstanding or a typo. If instead the $14 paid is 70% of the original price (implying only 30% off), then $14 equals 70% of the original price. In this case, dividing $14 by 0.70 gives the original price as $20, which matches one of the options.
Understanding the difference between “70% off” (meaning 70% discount) and “70% of the original price” (meaning 30% discount) is key here. The first implies paying 30%, and the second implies paying 70%.
Always carefully analyze the wording of discount problems. The formula to find original price when given discounted price is: Original Price=Discounted Price1−Discount Rate\text{Original Price} = \frac{\text{Discounted Price}}{1 – \text{Discount Rate}}
where discount rate is expressed as a decimal. For a 70% discount, that would be: Original Price=140.30=46.67\text{Original Price} = \frac{14}{0.30} = 46.67
For a 30% discount (70% of original price), it would be: Original Price=140.70=20\text{Original Price} = \frac{14}{0.70} = 20
So, based on the options given, the likely intended answer is B) 20.00.