Question

Each week, nia takes a violin lesson and a dance lesson. the dance lesson costs 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? choose 1 answer: a. d - v = 75 d = 2/3 v b. d - v = 75 v = 2/3 d c. d + v = 75

Answer 1

The system of equations that could be used to find the cost of the dance lesson and the violin lesson is v + (2/3)v = 75. Solving this equation yields the cost of the violin lesson as $45 and the cost of the dance lesson as $30.

Step-by-step explanation:

To find the cost of the dance lesson (d) and the violin lesson (v), we can set up a system of equations based on the given information. Let's say the cost of the violin lesson is v dollars.

According to the problem, the dance lesson costs 2/3 as much as the violin lesson, so the cost of the dance lesson would be (2/3)v dollars. The total cost of both lessons combined is $75, so we can set up the equation v + (2/3)v = 75.

Simplifying this equation, we have (5/3)v = 75. To solve for v, we multiply both sides of the equation by 3/5.

This gives us v = (75 * 3/5) = 45 dollars. Therefore, the cost of the violin lesson is $45.

To find the cost of the dance lesson, we substitute the value of v into the equation for the cost of the dance lesson, which is (2/3)v. Therefore, d = (2/3)(45) = 30 dollars.