Math Problem Statement

The cost of 3 tables and 5 chairs is PHP 600. The cost of 1 table and 2 chairs is Php 210. Find the cost of a table.

Solution

This is a system of equations problem. Let's break it down:

From the problem, we have two pieces of information:

  1. The cost of 3 tables and 5 chairs is PHP 600.
  2. The cost of 1 table and 2 chairs is PHP 210.

Let:

  • tt represent the cost of 1 table.
  • cc represent the cost of 1 chair.

We can write the problem as a system of equations:

3t + 5c &= 600 \quad \text{(Equation 1)} \\ t + 2c &= 210 \quad \text{(Equation 2)} \end{aligned}$$ To solve this, we can use the substitution or elimination method. I will use the substitution method for this example. ### Step 1: Solve Equation 2 for $$t$$ From Equation 2: $$t = 210 - 2c$$ ### Step 2: Substitute $$t$$ in Equation 1 Substitute $$t = 210 - 2c$$ into Equation 1: $$3(210 - 2c) + 5c = 600$$ Now, expand and simplify: $$630 - 6c + 5c = 600$$ $$630 - c = 600$$ $$-c = 600 - 630$$ $$-c = -30$$ $$c = 30$$ ### Step 3: Substitute $$c = 30$$ into Equation 2 Now that we know $$c = 30$$, substitute this into Equation 2 to find $$t$$: $$t + 2(30) = 210$$ $$t + 60 = 210$$ $$t = 210 - 60$$ $$t = 150$$ ### Final Answer: The cost of 1 table is PHP 150. Would you like more details or have any other questions on this? Here are some related questions to further explore the topic: 1. What would the cost of 4 tables and 3 chairs be based on the prices of a table and a chair? 2. How would you solve a system of equations with more than two variables? 3. Can you use matrices to solve this system of equations? 4. What happens if the total cost is changed (e.g., the total cost of 3 tables and 5 chairs becomes PHP 650)? 5. How would this problem be affected if you used a different method, like the elimination method? Tip: When solving systems of equations, it’s helpful to check your solution by plugging it back into the original equations to ensure it satisfies both.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Linear Equations

Formulas

Solving systems of linear equations using substitution method

Theorems

Basic properties of linear equations

Suitable Grade Level

Grades 7-9

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