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, Dakota shipped 1 small box and 9 large boxes, which cost her $121 to ship. Meanwhile, Abby shipped 7 small boxes and 5 large boxes, and paid $93. 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, Dakota shipped 1 small box and  9 large boxes, which cost her $121 to ship. Meanwhile, Abby shipped 7 small boxes and  5 large boxes, and paid $93. 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 variables: Let's define the variables for the cost to ship a small box as x and the cost to ship a large box as y. Dakota's shipment of 1 small box and 9 large boxes costing $121 can be represented by the equation: 1x + 9y = 121Represent Dakota's shipment: Similarly, Abby's shipment of 7 small boxes and 5 large boxes costing $93 can be represented by the equation: 7x + 5y = 93Create system of equations: We now have a system of two equations: 1x + 9y = 121 7x + 5y = 93 To use elimination, we need to make the coefficients of one of the variables the same in both equations. We can multiply the first equation by 7 to match the coefficient of x in the second equation.Use elimination method: Multiplying the first equation by 7 gives us: 7x + 63y = 847 Now we have the system: 7x + 63y = 847 7x + 5y = 93Eliminate x: To eliminate x, we subtract the second equation from the first: (7x + 63y) - (7x + 5y) = 847 - 93 7x + 63y - 7x - 5y = 847 - 93 58y = 754Solve for y: Solving for y, we divide both sides by 58: y = 754 / 58 y = 13Substitute back to solve for x: Now that we have the value for y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation: 1x + 9(13) = 121Final shipping costs: Simplify and solve for x: x + 117 = 121 x = 121 - 117 x = 4We have found the values for x and y: x = 4 (cost to ship a small box) y = 13 (cost to ship a large box) The shipping costs $4 for a small box and $13 for a large box.

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