Question #963da34c - SAT Suite Question Bank

ID: 963da34c

Modded SAT Question Bank by Abdullah Mallik

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?

$zero is less than x, which is less than or equal to 10$
$zero is less than x, which is less than or equal to 11 and two-thirds$
$zero is less than x, which is less than or equal to 17 and one-half$
$zero is less than x, which is less than or equal to 20$

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Correct Answer: A

Rationale

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 $2 times, open parenthesis, 2 point 5 x plus x, close parenthesis$ , 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 $7 x plus 60, is less than or equal to 130$ , or $7 x is less than or equal to 70$ . Dividing both sides of the inequality by 7 gives $x is less than or equal to 10$ . Since x represents the width of the box, x must also be a positive number. Therefore, the inequality $0 is less than x, which is less than or equal to 10$ 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.

Question Difficulty: Hard