WEBVTT
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A rectangular photograph measuring six centimeters by four centimeters is to be displayed in a card mount in a rectangular frame, as shown in the diagram.
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Which of the following equations can be used to find π₯ if the area of the mount is 64 centimeters squared?
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(A) Nine plus five π₯ times three plus seven π₯ minus 15 equals 18.
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(B) Five plus two π₯ times seven minus two π₯ minus 24 equals 28.
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(C) Three plus two π₯ times six minus five π₯ minus 21 equals 32.
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(D) Seven plus two π₯ times five plus two π₯ minus 13 equals 64.
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Or (E) four plus two π₯ times six plus two π₯ minus 24 equals 64.
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First, letβs think about what the area of the mount would be in the diagram.
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The area of the card mount would be this space.
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We can say that the card mount area will be equal to the area of the larger rectangle minus the area of the photograph.
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We know that for all rectangles, their area can be defined as the length times the width.
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The interior rectangle, the photograph, measures six centimeters by four centimeters.
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And therefore, its area can be found by multiplying six times four.
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For the larger rectangle, weβll need to think a bit more carefully.
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The distance lengthwise for the larger rectangle will be equal to π₯ plus six plus π₯.
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We can write that as six plus two π₯.
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Similarly, the width of the larger rectangle would then be equal to π₯ plus four plus π₯, which we can write as four plus two π₯.
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Our question says that the area of the mount is 64 centimeters squared.
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Our equation now looks like this: 64 equals six plus two π₯ times four plus two π₯ minus six times four.
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And six times four is 24.
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This exactly matches option (E).
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If we wanted to eliminate the other options, option (A) has terms with five π₯ and seven π₯, which do not match the larger rectangle.
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Option (B) have numbers five and seven, which we donβt find for the larger rectangle.
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Option (C) again has five π₯ and is using subtraction.
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Option (D) has five and seven and additionally is subtracting 13 for the area of the photograph, which again shows that the only viable option is option (E).
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Four plus two π₯ times six plus two π₯ minus 24 equals 64.