Question

(a) Write an equation that could be used to answer the question above.First, choose the appropriate form. Then, fill in the blanks with thenumbers 58, 8, and 6. Let b represent the number of books.+(b) Solve the equation in part (a) to find the number of books.b = 1

Answer 1

Writing equations

Part A

We know that on the right side of any of both equations must be the total cost of her purchase. On the left side must be the discount and the cost due to the books:

- Then,

58 must be on the right (since it is the total cost):

- Since each book costs $6 and she bought b (number of books), then the price due to the books is

$6b

- The discount is $8. It is the other part of the cost. Since it is a discount it must be a substraction "-":

Then the equation is

6b - 8 = 58

Answer: 6b - 8 = 58

Part B

In order to solve the equation

6b - 8 = 58

for b we want to "leave b alone" on one side of the equation.

In order to do that we just have to remember one simple rule:

Solving the equation

In order to "leave b alone" on the left side, we must take the 8 and 6 to the right:

6b - 8 = 58

↓ taking -8 to the right: we add 8 both sides

6b - 8 + 8 = 58 + 8

6b = 58 + 8 = 66

6b = 66

↓ taking 6 to the right: we divide 6 both sides

6b/6 = 66/6

b = 66/6 = 11

b = 11

Then, Debra bought 11 books.

Answer: b = 11