Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The Ashland High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Walton has requested 80 earth science textbooks and 92 physics textbooks for all of her classes, which costs the department a total of $7,744. Mr. Castro has asked for 80 earth science textbooks and 76 physics textbooks, which will cost a total of $6,912. How much do the textbooks cost? Earth science textbooks cost $_____ apiece and physics textbooks cost $_____ apiece.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The Ashland High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Walton has requested 80 earth science textbooks and 92 physics textbooks for all of her classes, which costs the department a total of $7,744. Mr. Castro has asked for 80 earth science textbooks and 76 physics textbooks, which will cost a total of $6,912. How much do the textbooks cost?  Earth science textbooks cost $_____ apiece and physics textbooks cost $_____ apiece.

Bytelearn · Accepted Answer

Define Costs: Let's denote the cost of one earth science textbook as x dollars and the cost of one physics textbook as y dollars. We can write two equations based on the information given: For Ms. Walton's request: 80 earth science textbooks and 92 physics textbooks cost a total of $7,744. For Mr. Castro's request: 80 earth science textbooks and 76 physics textbooks cost a total of $6,912.Write Equations: Translate the information into a system of equations: Ms. Walton's order: 80x + 92y = 7,744 Mr. Castro's order: 80x + 76y = 6,912Eliminate Variable: To use elimination, we need to eliminate one of the variables. Since the coefficient of x is the same in both equations, we can eliminate x by subtracting the second equation from the first. (80x + 92y) - (80x + 76y) = 7,744 - 6,912Subtract Equations: Perform the subtraction to find the value of y: 80x + 92y - 80x - 76y = 7,744 - 6,912 92y - 76y = 7,744 - 6,912 16y = 832 y = 832 / 16 y = 52Find y Value: Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use Ms. Walton's order: 80x + 92(52) = 7,744Substitute y: Calculate the value of x: 80x + 4,784 = 7,744 80x = 7,744 - 4,784 80x = 2,960 x = 2,960 / 80 x = 37Calculate x: We have found the values of x and y, which represent the cost of earth science and physics textbooks, respectively: x = 37 (cost of one earth science textbook) y = 52 (cost of one physics textbook)

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