Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ The Bloomington High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Sheppard has requested $77$ earth science textbooks and $85$ physics textbooks for all of her classes, which costs the department a total of $\$8,998$ . Mr. Blackburn has asked for $77$ earth science textbooks and $87$ physics textbooks, which will cost a total of $\$9,130$ . How much do the textbooks cost? $\newline$ Earth science textbooks cost $\$$ _ apiece and physics textbooks cost $\$$ _ apiece.

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

The Bloomington High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Sheppard has requested

77

earth science textbooks and

85

physics textbooks for all of her classes, which costs the department a total of

\$8,998

. Mr. Blackburn has asked for

77

earth science textbooks and

87

physics textbooks, which will cost a total of

\$9,130

. How much do the textbooks cost?

\newline

Earth science textbooks cost

\$

_____ apiece and physics textbooks cost

\$

_____ apiece.

Define variables: Define variables for the cost of each textbook type. Let $e$ be the cost of one earth science textbook and $p$ be the cost of one physics textbook. Ms. Sheppard's purchase gives the equation $77e + 85p = 8998$ .
Write equations: Write the equation for Mr. Blackburn's purchase, which is $77e + 87p = 9130$ .
Eliminate variable: To eliminate one variable, subtract Ms. Sheppard's equation from Mr. Blackburn's equation. This results in $0e + 2p = 132$ .
Solve for $p$ : Solve for $p$ by dividing the result of the subtraction by $2$ . This gives $p = 66$ .
Substitute and solve: Substitute $p = 66$ back into Ms. Sheppard's equation. This results in $77e + 85(66) = 8998$ .
Final solution: Solve for $e$ . First, calculate $85 \times 66 = 5610$ . Then, $8998 - 5610 = 3388$ . Finally, $3388 / 77 = 44$ .