A community library is moving its collection of books to a new building. The number of boo… — SAT

A community library is moving its collection of books to a new building. The number of books, $B$ , remaining to be packed $h$ hours after the packing begins is modeled by the linear equation $B = 12,500 - 450h$ , where $0 \leq h \leq 25$ . Which of the following is the best interpretation of $450$ in this context?

The number of books packed each hourAnswer
B
The initial number of books that need to be packed
C
The number of hours it takes to pack each book, which is $\frac{1}{450}$ hour
D
The total number of hours it takes to pack all the books

Answer

The number of books packed each hour

In the linear equation

B = 12,500 - 450h

, the coefficient of

h

-450

. This value represents the rate of change of the dependent variable,

B

(remaining books), with respect to the independent variable,

h

(hours). A slope of

-450

means that for every hour that passes, the number of remaining books decreases by

450

, which means

450

books are packed each hour.

Step-by-Step Solution

Identify the variable and constants in the given linear equation

B = 12,500 - 450h

B

represents the number of remaining books,

h

represents the number of hours spent packing,

12,500

is the constant term (

y

-intercept), and

-450

is the coefficient of

h

(slope).

Understanding the components of the linear model is essential to interpreting their real-world meanings.

Analyze the rate of change (slope) of the equation.

The slope is

-450

, which indicates that the number of remaining books decreases by

450

for every

1

hour that passes.

The coefficient of the independent variable in a linear equation in context represents the rate of change of the dependent variable with respect to the independent variable.

Translate the rate of change of the remaining books into the rate of packing.

A decrease of

450

remaining books per hour is equivalent to packing

450

books per hour.

Since books are being packed to be moved, a reduction in the remaining unpacked books corresponds directly to the number of books packed.

Key Concept

Interpreting the slope (rate of change) of a linear equation in a real-world context.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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