Question

Rocky Mcfist spends a total of $90 per week for karate lessons and ballet lessons. If the amount spent on karate lessons increases $10 per week, it will be two thirds of the amount spent on ballet lessons. How much does Rocky spend on ballet lessons?

Answer 1

Let x be the amount of money spent on karate lessons and y be the amount of money spent on ballet lessons (both per week).

1. Rocky Mcfist spends a total of $90 per week for karate lessons and ballet lessons. Then

$x+y=90.$

2. If the amount of money spent on karate lessons increases $10 per week, then it becomes x+10. It will be two thirds of the amount spent on ballet lessons, then

$x+10=\dfrac{2}{3}y.$

3. Solve the system of equations:

$\left\{\begin{array}{l}x+y=90\\ \\x+10=\dfrac{2}{3}y.\end{array}\right.$

From the second equation

$x=\dfrac{2}{3}y-10.$

Substitute this expression into the first equation

$\dfrac{2}{3}y-10+y=90|\cdot 3,\\ \\2y-30+3y=270,\\ \\2y+3y=270+30,\\ \\5y=300|:5,\\ \\y=60.$

Then

$x=\dfrac{2}{3}\cdot 60-10=2\cdot 20-10=40-10=30.$

Answer: Rocky spend on ballet lessons $60 per week.