Math Problem of the Week - Algebra and Up - May 8, 2022 to May 14, 2022

Algebra and Up: 

Question: Ten voice lessons and 5 piano lessons cost $368.75. Five piano lessons and 3 voice lessons cost $176.25. How much does a voice lesson cost?

Answer: $27.50

Solution: We can solve this system of equations problem with the elimination method. If v is the cost of a voice lesson and p is the cost of a piano lesson, then we know that 10v + 5p = 368.75 and 3v + 5p = 176.25. Notice that we have 5p in both equations, so we can subtract one whole equation from the other to leave us with one variable to solve for. If we subtract the smaller number of lessons, we’re left with 7v = 192.5. Therefore, a voice lesson costs $192.50 ÷ 7 = $27.50.