Question 15

Explanation

Problem Analysis

We can model this problem as a system of linear equations with two variables. Let the price of meat per kg be $x$ and the price of fish per kg be $y$ (in thousands of rupiah).

Formulating the Equations

From the data of Shop A, the sale of $80$ kg of meat and $20$ kg of fish results in $2960$ thousand rupiah:

Simplify this equation by dividing both sides by $20$:

From the data of Shop B, the sale of $70$ kg of meat and $40$ kg of fish results in $3040$ thousand rupiah:

Simplify this equation by dividing both sides by $10$:

Solving the System of Equations

We will eliminate variable $y$ to find the value of $x$. Multiply equation $(1)$ by $4$ so that the coefficient of $y$ matches equation $(2)$:

Subtract this resulting equation by equation $(2)$:

Determining the Price of Fish

Substitute the value $x = 32$ into equation $(1)$ to find $y$:

The value $y = 20$ means the price of fish is $20$ thousand rupiah or Rp20,000.00.