Math Problem Statement

Harga 2 pasang sepatu dan 3 pasang sandal adalah Rp 175.000,00, sedangkan harga 3 pasang sepatu dan 4 pasang sandal adalah Rp 255.000,00. Harga sepasang sepatu dan 2 pasang sandal adalah ....

Solution

The problem in the image can be solved using a system of linear equations. Let's define the variables:

  • Let xx be the price of one pair of shoes.
  • Let yy be the price of one pair of sandals.

We are given two pieces of information in the problem:

  1. The price of 2 pairs of shoes and 3 pairs of sandals is Rp 175,000: 2x+3y=175,0002x + 3y = 175,000

  2. The price of 3 pairs of shoes and 4 pairs of sandals is Rp 255,000: 3x+4y=255,0003x + 4y = 255,000

Now we have the system of equations:

2x + 3y &= 175,000 \\ 3x + 4y &= 255,000 \end{aligned}$$ We will solve this system to find $$x$$ (the price of one pair of shoes) and $$y$$ (the price of one pair of sandals). Once we find these values, we can calculate the price of one pair of shoes and two pairs of sandals, which is: $$x + 2y$$ Let's calculate this now.The solution to the system of equations gives: - The price of one pair of shoes ($$x$$) is Rp 65,000. - The price of one pair of sandals ($$y$$) is Rp 15,000. Therefore, the price of one pair of shoes and two pairs of sandals ($$x + 2y$$) is: $$65,000 + 2(15,000) = 95,000$$ Thus, the correct answer is **Rp 95,000** (option b). Do you have any questions or would you like further explanation? Here are some related questions you might consider: 1. How do you solve systems of equations with substitution? 2. What is the elimination method for solving simultaneous equations? 3. How can you check if a solution to a system of equations is correct? 4. What are some common mistakes in solving linear systems? 5. How can systems of equations be applied in real-world problems? **Tip:** When solving systems of equations, always double-check your results by substituting the solutions back into the original equations to verify accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
System of Linear Equations

Formulas

2x + 3y = 175,000
3x + 4y = 255,000
x + 2y

Theorems

Elimination method for solving simultaneous equations

Suitable Grade Level

Grades 6-8

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