Each week, Nia takes a violin lesson and a dance lesson. The dance lesson costs $$\dfrac{2}{3}$$ as much as the violin lesson, and the cost of both lessons combined is $$\$75$$. Which of the following systems of equations could be used to find $$d$$, the cost of the dance lesson in dollars, and $$v$$, the cost of the violin lesson in dollars?

Question

Each week, Nia takes a violin lesson and a dance lesson. The dance lesson costs    $$\dfrac{2}{3}$$ as much as the violin lesson, and the cost of both lessons combined is  $$\$75$$. Which of the following systems of equations could be used to find  $$d$$, the cost of the dance lesson in dollars, and  $$v$$, the cost of the violin lesson in dollars?

Bytelearn · Accepted Answer

Define variables:   Reasoning: Define variables for the costs. Let $d$ be the cost of the dance lesson and $v$ be the cost of the violin lesson.Write total cost equation:   Reasoning: Write the equation for the total cost. The total cost of both lessons is $75. Equation: $d + v = 75$Write cost relationship equation:   Reasoning: Write the equation for the cost relationship. The dance lesson costs $\dfrac{2}{3}$ as much as the violin lesson. Equation: $d = \dfrac{2}{3}v$Combine into system:   Reasoning: Combine the equations into a system. System of equations: 1. $d + v = 75$ 2. $d = \dfrac{2}{3}v$

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