Calculate the Price of Furniture with a 150% Markup: Determining Table and Chair Costs

Percentage Markup with Variable Relationships

The price of a table is 150% greater than the price of a chair.
Determine the individual prices for a table and a chair separately.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the cost of a table and a chair
00:07 Mark the chair's price with unknown X
00:13 From the given data, we can determine the table's price and express it using X
00:24 Convert percentages to fractions and simplify wherever possible
00:50 This is the expression for the table's price using X
00:59 Construct an appropriate equation based on the given data
01:07 Substitute the price expressions and solve for X
01:24 We want to isolate X
01:35 Let's isolate X
01:39 This is the chair's price
01:49 Insert this price into the table's price expression and solve
02:02 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The price of a table is 150% greater than the price of a chair.
Determine the individual prices for a table and a chair separately.

2

Step-by-step solution

To solve this problem, let's follow these steps:

  • Step 1: Define the variables. Assume the price of a chair is C C dollars.

  • Step 2: Determine the price increase for the table. Since the table's price is 150% greater than the chair's, calculate 150% of C C , given by 1.5×C 1.5 \times C .

  • Step 3: Compute the table's price. The price T T of the table is the sum of the chair's price and the calculated increase: T=C+1.5×C T = C + 1.5 \times C .

  • Step 4: Simplify the expression. This results in T=2.5×C T = 2.5 \times C .

Now, substituting values from the given options (since T=2.5×C T = 2.5 \times C ) reveals the following key information:

For option 3, with Chair at 100$ 100\$ , assuming Chair's price to be C=100 C = 100 :
T=2.5×100=250 T = 2.5 \times 100 = 250 .

Verification shows a chair price of 100$ 100\$ and table price of 250$ 250\$ as per our calculations. This matches our established equation, confirming it as the correct choice where a chair costs 100$ 100\$ and a table costs 250$ 250\$ .

Thus, the individual prices are C=100 dollars and T=250 dollars C = 100 \ \text{dollars and} \ T = 250 \ \text{dollars} , which aligns with option 3 in given choices.

3

Final Answer

Chair 100 $ and a table 150 $

Key Points to Remember

Essential concepts to master this topic
  • Definition: 150% greater means add 150% to original price
  • Formula: If chair = C, then table = C + 1.5C = 2.5C
  • Verification: Check that table price ÷ chair price = 2.5 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing '150% greater' with '150% of original price'
    Don't think 150% greater means table = 1.5 × chair = wrong answer! This gives table price that's only 50% more, not 150% more. Always remember '150% greater' means original + 150% = 2.5 times the original.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

What's the difference between '150% greater' and '150% of'?

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150% of means multiply by 1.5, but 150% greater means add 150% to the original. So if chair = $100, then 150% greater = $100 + (1.5 × $100) = $250!

How do I set up the equation when I don't know the actual prices?

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Use a variable! Let the chair price = C. Since table is 150% greater: Table = C + 1.5C = 2.5C. Now check which answer choice fits this relationship.

Why can't I just guess and check the answer choices?

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You can, but understanding the mathematical relationship helps you solve similar problems faster! Always verify that table price ÷ chair price = 2.5 for any correct answer.

What if the problem said '150% more expensive' instead?

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That's the same thing! '150% more expensive' and '150% greater' both mean you add 150% of the original price to get the new price.

How do I check my work without a calculator?

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Use the relationship: table price should be 2.5 times chair price. For option 3: $250 ÷ $100 = 2.5 ✓. Quick mental math works perfectly!

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