Calculate Total Cost: Finding Original Price from 35% Deposit of $3500

Q: Why do I divide by 0.35 instead of multiplying?

Because $3,500 already represents 35% of the total! Think of it like this: if 0.35 × Total = 3500, then Total = 3500 ÷ 0.35. Division 'undoes' the multiplication.

Q: How do I convert 35% to a decimal quickly?

Move the decimal point two places left: 35% → 3.5% → 0.35. Or just remember that % means 'out of 100', so $ 35\% = \frac{35}{100} = 0.35 $.

Q: Can I use a proportion instead?

Yes! Set up $ \frac{35}{100} = \frac{3500}{x} $, then cross-multiply: 35x = 350,000, so x = 10,000. Both methods work perfectly!

Q: How do I remember which number goes where?

Part over Whole always! The deposit ($3,500) is the part, and we're finding the whole (total price). So: $ \frac{\text{part}}{\text{whole}} = \frac{\text{percentage}}{100} $

Percentage Equations with Division Method

Kevin bought a computer and paid 3500 as a deposit. That sum is 35% of the total cost of the computer. Find the price of the computer.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the price of the computer

00:05 Construct the appropriate equation according to the given data

00:15 Use the formula to convert percentages to fractions

00:20 Apply this formula to our exercise

00:35 Isolate the computer price

01:10 Break down 3500 into factors of 35 and 100

01:17 Reduce wherever possible

01:30 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Kevin bought a computer and paid 3500 as a deposit. That sum is 35% of the total cost of the computer. Find the price of the computer.

Step-by-step solution

To solve this problem, we will use the percentage relationship:

Step 1: Convert the given percentage to a decimal:
35% as a decimal is $0.35$ because $35\% = \frac{35}{100}$ .
Step 2: Use the relationship between the deposit and the total cost:
The deposit is 35% of the total cost, so $0.35 \times \text{Total Cost} = 3500$ .
Step 3: Find the total cost by rearranging the formula and solving:
Hence, $\text{Total Cost} = \frac{3500}{0.35}$ .
Step 4: Calculate:
$\text{Total Cost} = \frac{3500}{0.35} = 10000$ .

Therefore, the price of the computer is $\text{\10,000} \)$ .

Final Answer

10000

Key Points to Remember

Essential concepts to master this topic

Rule: When part equals percentage of whole, divide part by decimal
Technique: Convert 35% to 0.35, then $\frac{3500}{0.35} = 10000$
Check: Verify that 35% of $10,000 equals$ 3,500: 0.35 × 10000 = 3500 ✓

Common Mistakes

Avoid these frequent errors

Multiplying instead of dividing to find the whole
Don't multiply 3500 × 0.35 = 1225! This gives you 35% of the deposit, not the total price. The deposit IS already 35% of the total. Always divide the part by the decimal percentage to find the whole.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I divide by 0.35 instead of multiplying?

Because $3,500 already represents 35% of the total! Think of it like this: if 0.35 × Total = 3500, then Total = 3500 ÷ 0.35. Division 'undoes' the multiplication.

How do I convert 35% to a decimal quickly?

Move the decimal point two places left: 35% → 3.5% → 0.35. Or just remember that % means 'out of 100', so $35\% = \frac{35}{100} = 0.35$ .

What if I get a weird decimal answer?

Always check if your decimal makes sense! In this problem, the total should be larger than the deposit. If you get something smaller than $3,500, you probably multiplied instead of divided.

Can I use a proportion instead?

Yes! Set up $\frac{35}{100} = \frac{3500}{x}$ , then cross-multiply: 35x = 350,000, so x = 10,000. Both methods work perfectly!

How do I remember which number goes where?

Part over Whole always! The deposit (3,500) is the part, and we're finding the whole (total price). So: $\( \frac{\text{part}}{\text{whole}} = \frac{\text{percentage}}{100}$

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