Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Parent 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, 26 basic yearbooks and 16 deluxe yearbooks were ordered, for a total of $3,326. The students in Mr. Erickson's class ordered 26 basic yearbooks and 15 deluxe yearbooks, for a total of $3,227. How much does each option cost?The basic yearbook costs $_____, and the deluxe yearbook costs $_____.
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Parent 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, 26 basic yearbooks and 16 deluxe yearbooks were ordered, for a total of $3,326. The students in Mr. Erickson's class ordered 26 basic yearbooks and 15 deluxe yearbooks, for a total of $3,227. How much does each option cost?The basic yearbook costs $_____, and the deluxe yearbook costs $_____.
Define Variables: Let's denote the cost of the basic yearbook as x dollars and the cost of the deluxe yearbook as y dollars.The total cost of yearbooks in Mrs. Williamson's class can be represented by the equation:26x+16y=3326
Formulate Equations: Similarly, the total cost of yearbooks in Mr. Erickson's class can be represented by the equation: 26x+15y=3227
Eliminate Variable: We now have a system of equations to solve:26x+16y=332626x+15y=3227To solve for x and y, we can subtract the second equation from the first to eliminate x.(26x+16y)−(26x+15y)=3326−3227
Simplify Equation: Simplify the equation from Step 3:26x+16y−26x−15y=3326−322716y−15y=3326−3227y=99
Substitute and Solve: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the second equation: 26x+15(99)=3227
Finalize Values: Simplify the equation from Step 5 to solve for x:26x+1485=322726x=3227−148526x=1742x=261742x=67
Finalize Values: Simplify the equation from Step 5 to solve for x:26x+1485=322726x=3227−148526x=1742x=261742x=67We have found the values of x and y:x=67 (the cost of the basic yearbook)y=99 (the cost of the deluxe yearbook)
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