Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The Richmond High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Lee has requested 83 earth science textbooks and 65 physics textbooks for all of her classes, which costs the department a total of $7,072. Mr. Barrett has asked for 83 earth science textbooks and 83 physics textbooks, which will cost a total of $8,134. 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 Richmond High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Lee has requested 83 earth science textbooks and 65 physics textbooks for all of her classes, which costs the department a total of $7,072. Mr. Barrett has asked for 83 earth science textbooks and 83 physics textbooks, which will cost a total of $8,134. How much do the textbooks cost?  Earth science textbooks cost $_____ apiece and physics textbooks cost $_____ apiece.

Bytelearn · Accepted Answer

Define variables: Let's define two variables: let x be the cost of one earth science textbook, and y be the cost of one physics textbook.Write equations: We can write two equations based on the information given. For Ms. Lee's request, the equation is 83x + 65y = 7,072. For Mr. Barrett's request, the equation is 83x + 83y = 8,134.Use elimination: To use elimination, we need to make the coefficients of one of the variables the same in both equations. The coefficients of x are already the same, so we can subtract the first equation from the second to eliminate x.Subtract equations: Subtracting the first equation from the second gives us 83x + 83y - (83x + 65y) = 8,134 - 7,072.Simplify equation: This simplifies to 83y - 65y = 8,134 - 7,072, which further simplifies to 18y = 1,062.Find cost of physics textbook: Dividing both sides of the equation by 18 gives us y = 1,062 / 18, which simplifies to y = 59. This means that each physics textbook costs $59.Substitute value of y: Now that we know the cost of each physics textbook, we can substitute y = 59 into one of the original equations to find x. Let's use the first equation: 83x + 65(59) = 7,072.Solve for x: Substituting the value of y into the equation gives us 83x + 3,835 = 7,072.Subtracting 3,835 from both sides of the equation gives us 83x = 7,072 - 3,835, which simplifies to 83x = 3,237.Dividing both sides of the equation by 83 gives us x = 3,237 / 83, which simplifies to x = 39. This means that each earth science textbook costs $39.

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