Section A Section A Checkpoint

Problem 1

An artist is creating a piece that will begin as a square piece of paper that is 17 inches on each side. They will print text on a portion of the paper, leaving some white space on each side. The spaces on the top and bottom of the paper will be equal and the spaces to the left and right will each be twice as much as on the top and bottom.

The area of the printed text is 130 square inches.

Write an equation that represents the printed area.
The approximate solutions are $x = 1.82$ and $x = 10.93$ . Do these solutions make sense in this situation? Explain your reasoning.

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Solution

$(17-2x)(17-4x)=130$
1.82 makes sense, but 10.93 does not. Sample reasoning: When $x = 1.82$ , one side of the printed area will be 13.36 inches ( $17 - 2\boldcdot 1.82 = 13.36$ ) and the other side of the printed area will be 9.72 inches ( $17-4\boldcdot 1.82 = 9.72$ ). If $x = 10.93$ , then there is more than 20 inches of margin on the top and bottom together, but the page is only 17 inches tall.

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Sample Response

$(17-2x)(17-4x)=130$
1.82 makes sense, but 10.93 does not. Sample reasoning: When $x = 1.82$ , one side of the printed area will be 13.36 inches ( $17 - 2\boldcdot 1.82 = 13.36$ ) and the other side of the printed area will be 9.72 inches ( $17-4\boldcdot 1.82 = 9.72$ ). If $x = 10.93$ , then there is more than 20 inches of margin on the top and bottom together, but the page is only 17 inches tall.