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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe Bloomington High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Sheppard has requested 7777 earth science textbooks and 8585 physics textbooks for all of her classes, which costs the department a total of $8,998\$8,998. Mr. Blackburn has asked for 7777 earth science textbooks and 8787 physics textbooks, which will cost a total of $9,130\$9,130. How much do the textbooks cost?\newlineEarth science textbooks cost $\$_____ apiece and physics textbooks cost $\$_____ apiece.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe Bloomington High School Science Department is purchasing new earth science and physics textbooks this year. Ms. Sheppard has requested 7777 earth science textbooks and 8585 physics textbooks for all of her classes, which costs the department a total of $8,998\$8,998. Mr. Blackburn has asked for 7777 earth science textbooks and 8787 physics textbooks, which will cost a total of $9,130\$9,130. How much do the textbooks cost?\newlineEarth science textbooks cost $\$_____ apiece and physics textbooks cost $\$_____ apiece.
  1. Define variables: Define variables for the cost of each textbook type. Let ee be the cost of one earth science textbook and pp be the cost of one physics textbook. Ms. Sheppard's purchase gives the equation 77e+85p=899877e + 85p = 8998.
  2. Write equations: Write the equation for Mr. Blackburn's purchase, which is 77e+87p=913077e + 87p = 9130.
  3. Eliminate variable: To eliminate one variable, subtract Ms. Sheppard's equation from Mr. Blackburn's equation. This results in 0e+2p=1320e + 2p = 132.
  4. Solve for pp: Solve for pp by dividing the result of the subtraction by 22. This gives p=66p = 66.
  5. Substitute and solve: Substitute p=66p = 66 back into Ms. Sheppard's equation. This results in 77e+85(66)=899877e + 85(66) = 8998.
  6. Final solution: Solve for ee. First, calculate 85×66=561085 \times 66 = 5610. Then, 8998−5610=33888998 - 5610 = 3388. Finally, 3388/77=443388 / 77 = 44.

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