Question

1. mr. johnson shipped a box of math textbooks and novels to a colleague. each math textbook weighed 2.5 pounds, and each novel weighed 1.25 pounds. there were a total of 18 books, with a total weight of 31.25 pounds.

a. write a system of equations that models this scenario. set up and identify your variables.
b. solve your system of equations from part a.
c. explain what the solution to system means.

Explanation:

Part A

Step1: Define variables

Let $x$ = number of math textbooks, $y$ = number of novels.

Step2: Total books equation

Total books: $x + y = 18$

Step3: Total weight equation

Total weight: $2.5x + 1.25y = 31.25$

Part B

Step1: Isolate $y$ from first eq

$y = 18 - x$

Step2: Substitute into second eq

$2.5x + 1.25(18 - x) = 31.25$

Step3: Simplify and solve for $x$

$2.5x + 22.5 - 1.25x = 31.25$
$1.25x = 31.25 - 22.5$
$1.25x = 8.75$
$x = \frac{8.75}{1.25} = 7$

Step4: Solve for $y$

$y = 18 - 7 = 11$

Part C

Step1: Interpret solution values

The values of $x$ and $y$ represent the count of each book type in the shipped box.

Answer:

A. Variables: $x$ = number of math textbooks, $y$ = number of novels
System of equations:

$$\begin{cases} x + y = 18 \\ 2.5x + 1.25y = 31.25 \end{cases}$$

B. $x = 7$, $y = 11$
C. The solution means Mr. Johnson shipped 7 math textbooks and 11 novels in the box.