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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions