Gina wants to take dance classes. She compares two dance studios to determine which had the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.

Dance World: y=15x
Toe Tappers: y=25 + 12.5x

How many classes would Gina need to take for the total cost to be the same at both dance studios?

For 10 classes would Gina need to take for the total cost to be the same at both dance studios .

Step-by-step explanation:

Here we have , Gina wants to take dance classes. She compares two dance studios to determine which had the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.

Dance World: y=15x

Toe Tappers: y=25 + 12.5x

We need to find How many classes would Gina need to take for the total cost to be the same at both dance studios . Let's find out ;

According to question , We need to find the classes for which cost is equal i.e.

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Therefore ,for 10 classes would Gina need to take for the total cost to be the same at both dance studios .

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15