Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The cheerleaders from Centerville High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped 36 small clothing boxes and 17 large clothing boxes, using a total of 441 feet of wrapping paper. The day before, they wrapped 33 small clothing boxes and 38 large clothing boxes, using a total of 606 feet of gift wrap. How much paper does it take to wrap each size of box? Each small box uses _____ feet of paper and each large one uses _____ feet.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The cheerleaders from Centerville High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped 36 small clothing boxes and  17 large clothing boxes, using a total of 441 feet of wrapping paper. The day before, they wrapped 33 small clothing boxes and  38 large clothing boxes, using a total of 606 feet of gift wrap. How much paper does it take to wrap each size of box?  Each small box uses _____ feet of paper and each large one uses _____ feet.

Bytelearn · Accepted Answer

Define variables: Define the variables for the system of equations. Let x be the amount of paper needed to wrap a small box. Let y be the amount of paper needed to wrap a large box.Write equations: Write the equations based on the given information. Yesterday's wrapping: 36 small boxes and 17 large boxes used 441 feet of paper. The day before: 33 small boxes and 38 large boxes used 606 feet of paper. This gives us the system of equations: 36x + 17y = 441 33x + 38y = 606Eliminate variable: Choose which variable to eliminate and decide on the operation to use. We can choose to eliminate either x or y. To eliminate x, we can multiply the first equation by 33 and the second equation by 36 to make the coefficients of x the same.Multiply equations: Multiply the equations to make the coefficients of x the same. First equation multiplied by 33: (36x + 17y) * 33 = 441 * 33 1188x + 561y = 14553  Second equation multiplied by 36: (33x + 38y) * 36 = 606 * 36 1188x + 1368y = 21816Subtract to eliminate: Subtract the second equation from the first to eliminate x. 1188x + 561y - (1188x + 1368y) = 14553 - 21816 1188x + 561y - 1188x - 1368y = 14553 - 21816 -807y = -7263Solve for y: Solve for y. -807y = -7263 y = -7263 / -807 y = 9Substitute and solve: Substitute the value of y into one of the original equations to solve for x. Using the first equation: 36x + 17(9) = 441 36x + 153 = 441 36x = 441 - 153 36x = 288Solve for x: Solve for x. 36x = 288 x = 288 / 36 x = 8Final answer: Write the final answer. Each small box uses 8 feet of paper and each large one uses 9 feet.

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