Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The postal service offers flat-rate shipping for priority mail in special boxes. Today, Jamal shipped 7 small boxes and 4 large boxes, which cost him $68 to ship. Meanwhile, Brian shipped 1 small box and 5 large boxes, and paid $54. How much does it cost to ship these two sizes of box? Shipping costs $_____ for a small box and $_____ for a large box.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The postal service offers flat-rate shipping for priority mail in special boxes. Today, Jamal shipped 7 small boxes and  4 large boxes, which cost him $68 to ship. Meanwhile, Brian shipped 1 small box and  5 large boxes, and paid $54. How much does it cost to ship these two sizes of box?  Shipping costs $_____ for a small box and  $_____ for a large box.

Bytelearn · Accepted Answer

Define Equations: Let's denote the cost to ship a small box as x dollars and the cost to ship a large box as y dollars. We can write two equations based on the information given: For Jamal: 7 small boxes + 4 large boxes = $68 For Brian: 1 small box + 5 large boxes = $54 This translates to the system of equations: 7x + 4y = 68 x + 5y = 54Use Elimination Method: To use elimination, we need to make the coefficients of one of the variables the same in both equations. We can multiply the second equation by 7 to match the coefficient of x in the first equation: 7(1x + 5y) = 7(54) This gives us: 7x + 35y = 378Perform Subtraction: Now we have the system of equations: 7x + 4y = 68 7x + 35y = 378 We can eliminate x by subtracting the first equation from the second equation: (7x + 35y) - (7x + 4y) = 378 - 68Solve for y: Perform the subtraction to solve for y: 7x + 35y - 7x - 4y = 378 - 68 31y = 310 Now, divide both sides by 31 to find y: y = 310 / 31 y = 10Substitute to Find x: Now that we have the value of y, we can substitute it back into one of the original equations to find x. Let's use the second equation: x + 5y = 54 x + 5(10) = 54 x + 50 = 54 Subtract 50 from both sides to solve for x: x = 54 - 50 x = 4Final Cost Solution: We have found the values of x and y: x = 4 (cost to ship a small box) y = 10 (cost to ship a large box) This means it costs $4 to ship a small box and $10 to ship a large box.

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