Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The cheerleaders from Hampton High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped 40 small clothing boxes and 20 large clothing boxes, using a total of 400 feet of wrapping paper. The day before, they wrapped 40 small clothing boxes and 35 large clothing boxes, using a total of 580 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 Hampton High School are doing a giftwrapping fundraiser at a clothing store. Yesterday, they wrapped 40 small clothing boxes and  20 large clothing boxes, using a total of 400 feet of wrapping paper. The day before, they wrapped 40 small clothing boxes and  35 large clothing boxes, using a total of 580 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 and Equations:  Step 1: Define the variables and set up the equations based on the given information. Let x be the amount of paper needed for each small box, and y be the amount for each large box. From the first day: 40 small boxes and 20 large boxes used 400 feet of paper. Equation: 40x + 20y = 400 From the previous day: 40 small boxes and 35 large boxes used 580 feet of paper. Equation: 40x + 35y = 580Simplify Equations:  Step 2: Simplify both equations to make the numbers smaller and easier to work with. Divide the first equation by 20: 2x + y = 20 Divide the second equation by 5: 8x + 7y = 116Use Elimination Method:  Step 3: Use elimination to solve for one variable. We'll eliminate y by making the coefficients of y equal in both equations. Multiply the first simplified equation by 7: 14x + 7y = 140 Now subtract this new equation from the second simplified equation: 8x + 7y = 116 (8x + 7y) - (14x + 7y) = 116 - 140 -6x = -24Solve for x:  Step 4: Solve for x. Divide both sides by -6: x = 4Substitute to Find y:  Step 5: Substitute x = 4 back into one of the simplified equations to find y. Using 2x + y = 20: 2(4) + y = 20 8 + y = 20 y = 12

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