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Linear inequalities in one or two variables SAT question
Math · Algebra · Hard · Answer it here, explanation included.
A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?
ExplanationShow
Choice A is correct. If x is the width, in inches, of the box, then the length of the box is 2.5x inches. It follows that the perimeter of the base is 
, or 7x inches. The height of the box is given to be 60 inches. According to the restriction, the sum of the perimeter of the base and the height of the box should not exceed 130 inches. Algebraically, this can be represented by 
, or 
. Dividing both sides of the inequality by 7 gives 
. Since x represents the width of the box, x must also be a positive number. Therefore, the inequality 
represents all the allowable values of x that satisfy the given conditions.
Choices B, C, and D are incorrect and may result from calculation errors or misreading the given information.
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