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John spent 40 percent of his earnings last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earnings did John have left over?
- a)30%
- b)32%
- c)45%
- d)68%
- e)70%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
John spent 40 percent of his earnings last month on rent and 30 percen...
Step 1: Analyze the Question
John spends 40% on one thing and 30% less than that on another. Since the answer choices are percents, picking 100 is a good idea. Some answer choices are widely spread out. When choices are spread out, estimation and logic are also great approaches.
John spends 40% on one thing and 30% less than that on another. Since the answer choices are percents, picking 100 is a good idea. Some answer choices are widely spread out. When choices are spread out, estimation and logic are also great approaches.
Step 2: State the Task
What percent of last month's earnings did John have left over? We now know that we'd pick $100 as his earnings. (We care much more about picking manageable numbers than about giving imaginary people a living wage.) It's also important to focus on the fact that we are solving for what he has left after paying for rent and the dishwasher, not what he spent on those things.
What percent of last month's earnings did John have left over? We now know that we'd pick $100 as his earnings. (We care much more about picking manageable numbers than about giving imaginary people a living wage.) It's also important to focus on the fact that we are solving for what he has left after paying for rent and the dishwasher, not what he spent on those things.
Step 3: Approach Strategically
Some answer choices could be logically eliminated right away. After spending 40% of his earnings on rent, he'd have 60% left. Then he spends some more. Therefore, no answer 60% or greater could be possible. That eliminates (D) and (E) very quickly. And since simple combinations of percents are rarely the right answer, the odds of the right answer being “subtract 40% and then subtract 30%" are very small. That makes 100% - 40% - 30% = 30%, choice (A), a safe elimination as well. We could make a 50/50 guess very quickly on this problem, which is sometimes a good thing to do if you are falling behind pace. But let's say that you had the time to solve. Picking $100 for his earnings, we see that John spends $40 on rent. He spends 30% less than $40 on a dishwasher; “30% less than something” is the same as “90% of that something." So John spent 0.7($40), or $28, on a dishwasher. Taking $40 and $28, or $68 away from $100, John is left with $32. That's 32% of his original earnings, so choice (B) is correct.
Some answer choices could be logically eliminated right away. After spending 40% of his earnings on rent, he'd have 60% left. Then he spends some more. Therefore, no answer 60% or greater could be possible. That eliminates (D) and (E) very quickly. And since simple combinations of percents are rarely the right answer, the odds of the right answer being “subtract 40% and then subtract 30%" are very small. That makes 100% - 40% - 30% = 30%, choice (A), a safe elimination as well. We could make a 50/50 guess very quickly on this problem, which is sometimes a good thing to do if you are falling behind pace. But let's say that you had the time to solve. Picking $100 for his earnings, we see that John spends $40 on rent. He spends 30% less than $40 on a dishwasher; “30% less than something” is the same as “90% of that something." So John spent 0.7($40), or $28, on a dishwasher. Taking $40 and $28, or $68 away from $100, John is left with $32. That's 32% of his original earnings, so choice (B) is correct.
Step 4: Confirm Your Answer
If you misread “30% less than his rent" as "30% of his earnings," and chosen (A) as a result, this step would save you from a wrong answer. Also, (D) is another trap answer that represents the total percentage of this earnings that John spent.
If you misread “30% less than his rent" as "30% of his earnings," and chosen (A) as a result, this step would save you from a wrong answer. Also, (D) is another trap answer that represents the total percentage of this earnings that John spent.
Most Upvoted Answer
John spent 40 percent of his earnings last month on rent and 30 percen...
To solve this problem, we need to calculate the percentage of John's earnings that he spent on rent and the percentage he spent on the dishwasher. Then, we can subtract these percentages from 100% to find out how much he had left over.
Let's assume John's earnings last month were $100.
1. Calculate the amount John spent on rent:
- John spent 40% of his earnings on rent.
- 40% of $100 = $40
2. Calculate the amount John spent on the dishwasher:
- John spent 30% less than what he spent on rent.
- 30% of $40 = $12 (the amount he spent less)
- Amount spent on dishwasher = $40 - $12 = $28
3. Calculate the percentage of John's earnings that he spent on the dishwasher:
- $28 (amount spent on dishwasher) / $100 (earnings) * 100 = 28%
4. Calculate the percentage of John's earnings that he had left over:
- 100% (total earnings) - 40% (rent) - 28% (dishwasher) = 32%
Therefore, John had 32% of his earnings left over.
Key Points:
- John spent 40% of his earnings on rent.
- He spent 30% less than the amount spent on rent on purchasing a dishwasher.
- To find the percentage of earnings left over, subtract the percentages spent on rent and the dishwasher from 100%.
Let's assume John's earnings last month were $100.
1. Calculate the amount John spent on rent:
- John spent 40% of his earnings on rent.
- 40% of $100 = $40
2. Calculate the amount John spent on the dishwasher:
- John spent 30% less than what he spent on rent.
- 30% of $40 = $12 (the amount he spent less)
- Amount spent on dishwasher = $40 - $12 = $28
3. Calculate the percentage of John's earnings that he spent on the dishwasher:
- $28 (amount spent on dishwasher) / $100 (earnings) * 100 = 28%
4. Calculate the percentage of John's earnings that he had left over:
- 100% (total earnings) - 40% (rent) - 28% (dishwasher) = 32%
Therefore, John had 32% of his earnings left over.
Key Points:
- John spent 40% of his earnings on rent.
- He spent 30% less than the amount spent on rent on purchasing a dishwasher.
- To find the percentage of earnings left over, subtract the percentages spent on rent and the dishwasher from 100%.
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