Tanya read 12 books for extra credit. She received 3.5 points for each nonfiction book and 1.5 points for each fiction book. If she received 28 extra credit points, how many of each kind of book did Tonya read?

Tanya read 5 nonfiction books and 7 fiction books.

Step-by-step explanation:

Given that:

Number of books read by Tanya = 12

Points for nonfiction book = 3.5

Points for fiction book = 1.5

Total credit points received = 28

Let,

x be the number of nonfiction book read

y be the number fiction books read

According to given statement;

x+y=12     Eqn 1

3.5x+1.5y=28    Eqn 2

Multiplying Eqn 1 by 1.5

1.5(x+y=12)

1.5x+1.5y=18    Eqn 3

Subtracting Eqn 3 from Eqn 2

(3.5x+1.5y)-(1.5x+1.5y)=28-18

3.5x+1.5y-1.5x-1.5y=10

2x=10

Dividing both sides by 2

Putting x=5 in Eqn 1

5+y=12

y=12-5

y=7

Hence,

Tanya read 5 nonfiction books and 7 fiction books.

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