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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineParent volunteers at Westford High School are processing yearbook order forms. Students have an option to get the basic yearbook or a deluxe option, which includes engraving and a protective cover. In Mrs. Williamson's class, 2626 basic yearbooks and 1616 deluxe yearbooks were ordered, for a total of $3,326\$3,326. The students in Mr. Erickson's class ordered 2626 basic yearbooks and 1515 deluxe yearbooks, for a total of $3,227\$3,227. How much does each option cost?\newlineThe basic yearbook costs $\$_____, and the deluxe yearbook costs $\$_____.

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineParent volunteers at Westford High School are processing yearbook order forms. Students have an option to get the basic yearbook or a deluxe option, which includes engraving and a protective cover. In Mrs. Williamson's class, 2626 basic yearbooks and 1616 deluxe yearbooks were ordered, for a total of $3,326\$3,326. The students in Mr. Erickson's class ordered 2626 basic yearbooks and 1515 deluxe yearbooks, for a total of $3,227\$3,227. How much does each option cost?\newlineThe basic yearbook costs $\$_____, and the deluxe yearbook costs $\$_____.
  1. Define Variables: Let's denote the cost of the basic yearbook as xx dollars and the cost of the deluxe yearbook as yy dollars.\newlineThe total cost of yearbooks in Mrs. Williamson's class can be represented by the equation:\newline26x+16y=332626x + 16y = 3326
  2. Formulate Equations: Similarly, the total cost of yearbooks in Mr. Erickson's class can be represented by the equation: 26x+15y=322726x + 15y = 3227
  3. Eliminate Variable: We now have a system of equations to solve:\newline26x+16y=332626x + 16y = 3326\newline26x+15y=322726x + 15y = 3227\newlineTo solve for xx and yy, we can subtract the second equation from the first to eliminate xx.\newline(26x+16y)(26x+15y)=33263227(26x + 16y) - (26x + 15y) = 3326 - 3227
  4. Simplify Equation: Simplify the equation from Step 33:\newline26x+16y26x15y=3326322726x + 16y - 26x - 15y = 3326 - 3227\newline16y15y=3326322716y - 15y = 3326 - 3227\newliney=99y = 99
  5. Substitute and Solve: Now that we have the value of yy, we can substitute it back into one of the original equations to solve for xx. Let's use the second equation: 26x+15(99)=322726x + 15(99) = 3227
  6. Finalize Values: Simplify the equation from Step 55 to solve for xx:26x+1485=322726x + 1485 = 322726x=3227148526x = 3227 - 148526x=174226x = 1742x=174226x = \frac{1742}{26}x=67x = 67
  7. Finalize Values: Simplify the equation from Step 55 to solve for xx:26x+1485=322726x + 1485 = 322726x=3227148526x = 3227 - 148526x=174226x = 1742x=174226x = \frac{1742}{26}x=67x = 67We have found the values of xx and yy:x=67x = 67 (the cost of the basic yearbook)y=99y = 99 (the cost of the deluxe yearbook)

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