Question

The Learning Center charges a one-time fee of $26 plus $10 per piano lesson. Guitar lessons have a one-time fee of $36 plus $8 for each lesson. After how many lessons will the cost of learning to play piano be the same or more than learning to play guitar

Answer 1

Given :

The Learning Center charges a one-time fee of $26 plus $10 per piano lesson.

Guitar lessons have a one-time fee of $36 plus $8 for each lesson.

To Find :

After how many lessons will the cost of learning to play piano be the same or more than learning to play guitar.

Solution :

Mathematical expression of piano lesson :

$P_1=26+10x$

Mathematical expression of guitar lesson :

$P_2=36+8y$

( Here, x and y are number of lessons )

Let, after t hours cost of learning to play piano be the same or more than learning to play guitar.

Now, given constraint :

$P_1 \geq P_2\\\\26+10t \geq 36+8t\\\\2t \geq 10\\\\t\geq 5$

Hence, this is the required solution.