Calculate Individual Shares: Dividing $7000 with Percentages

Percentage Calculations with Remainder Finding

7000 $ was shared between three people.

The first person received 40% of the total, the second person received 15% of the total and the third person received the remainder.

How much money did they each receive?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 How much money did each one receive?
00:06 Convert percentages to fractions and multiply by the total amount
00:23 Break down into factors and reduce wherever possible
00:28 This is the amount that the first one received
00:37 Apply the same method in order to determine the amount for the second one
00:40 Convert percentages to fractions and multiply by the total amount
00:44 Break down into factors and reduce wherever possible
00:49 This is the amount that the second one received
00:58 In order to determine the third amount, proceed to subtract the two amounts from the total
01:14 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7000 $ was shared between three people.

The first person received 40% of the total, the second person received 15% of the total and the third person received the remainder.

How much money did they each receive?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Determine how much the first person receives by calculating 40% of 7000.</li><li>Step2:Determinehowmuchthesecondpersonreceivesbycalculating157000.</li> <li>Step 2: Determine how much the second person receives by calculating 15% of 7000.
  • Step 3: Calculate the amount the third person receives by finding the remainder after the first two allocations.

Let's proceed with each step:
Step 1: Calculate 40% of 7000. The formula to use is:

\( \text{Amount} = \frac{40}{100} \times 7000 = 2800

Thus, the first person receives 2800</strong>.</p><p><strong>Step2:</strong>Calculate152800</strong>.</p> <p><strong>Step 2:</strong> Calculate 15% of 7000. Using the same formula:

Amount=15100×7000=1050 \text{Amount} = \frac{15}{100} \times 7000 = 1050

Therefore, the second person receives 1050.

Step 3: Calculate the remaining amount for the third person:

\( \text{Remainder} = 7000 - (2800 + 1050) = 3150

This means the third person receives 3150</strong>.</p><p>Toconfirm,thetotal3150</strong>.</p> <p>To confirm, the total 7000 is distributed correctly as 2800+1050+3150=70002800 + 1050 + 3150 = 7000.

Thus, the amount received by each person is:

  • The first person received 2800.</li><li>Thesecondpersonreceived2800.</li> <li>The second person received 1050.
  • The third person received $3150.

Therefore, the correct solution is choice #3.

3

Final Answer

The first person received 2800 dollars: the second person received 1050 dollars and the third person received 3150 dollars.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert percentages to decimals by dividing by 100
  • Technique: Calculate 40% of 7000 as \( \frac{40}{100} \times 7000 = 2800
  • Check: All shares must add up to the total: 2800+2800 + 1050 + 3150=3150 = 7000 ✓

Common Mistakes

Avoid these frequent errors
  • Calculating percentages of wrong amounts
    Don't calculate the third person's percentage from remaining money like 45% of 3150=3150 = 1417.50! This is wrong because percentages are always calculated from the original total. Always calculate each percentage from the full $7000, then find the remainder by subtraction.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why don't I calculate 45% for the third person since 40% + 15% = 55% and 100% - 55% = 45%?

+

Great thinking! You're right that the third person gets 45% of the total. You could calculate 45100×7000=3150 \frac{45}{100} \times 7000 = 3150 , but it's often safer to subtract to avoid calculation errors.

How do I convert percentages to decimals quickly?

+

Move the decimal point two places to the left! So 40% becomes 0.40, and 15% becomes 0.15. Then multiply: 0.40 × 7000 = 2800.

What if the percentages don't add up to 100%?

+

Check your problem again! In sharing problems, the percentages should always add up to 100%. If they don't, you might have misread the question.

Can I solve this without calculating percentages?

+

You could set up equations, but percentage calculation is much simpler here! The method shown is the most direct approach for this type of problem.

How do I know which answer choice is correct?

+

Calculate each person's share step by step, then compare your results to the answer choices. Also verify that your three amounts add up to $7000!

What if I get decimal amounts when calculating percentages?

+

That's normal! Many real-world percentage problems result in decimal amounts. Just round to the nearest cent (two decimal places) when dealing with money.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Percentage questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Quantity, percentage, percentage value

Convert Fraction to Percentage: Solving 15/20 Step-by-Step
Click to solve
Calculate Dance Class Attendance: Solve 16% of 9th Graders Problem
Click to solve