A graphic designer is exporting images for a website. There are two types of images: stand… — SAT

A graphic designer is exporting images for a website. There are two types of images: standard images and high-resolution images. Each standard image, $x$ , requires 3 megabytes (MB) of storage and takes 2 seconds to upload. Each high-resolution image, $y$ , requires 8 MB of storage and takes 5 seconds to upload. The designer must limit the total storage of the exported images to at most 120 MB and the total upload time to at least 60 seconds. Which of the following systems of inequalities models this situation?

A
$3x + 2y \leq 120$
$8x + 5y \geq 60$
B
$3x + 8y \geq 120$
$2x + 5y \leq 60$
C
$8x + 3y \leq 120$
$5x + 2y \geq 60$
$3x + 8y \leq 120$
$2x + 5y \geq 60$ Answer

Answer

The system of inequalities is

3x + 8y \leq 120

and

2x + 5y \geq 60

The correct system models the limits correctly. The storage constraint is represented by

3x + 8y \leq 120

since 'at most' corresponds to a less-than-or-equal-to sign. The upload time constraint is represented by

2x + 5y \geq 60

since 'at least' corresponds to a greater-than-or-equal-to sign.

Step-by-Step Solution

Set up the inequality for the storage constraint.

3x + 8y \leq 120

Each standard image uses 3 megabytes and each high-resolution image uses 8 megabytes. The total storage must be at most (less than or equal to) 120 megabytes.

Set up the inequality for the upload time constraint.

2x + 5y \geq 60

Each standard image takes 2 seconds and each high-resolution image takes 5 seconds to upload. The total upload time must be at least (greater than or equal to) 60 seconds.

Combine both inequalities into a system.

The system containing

3x + 8y \leq 120

and

2x + 5y \geq 60

Both constraints must be satisfied simultaneously.

Key Concept

Translating verbal constraints into systems of linear inequalities in two variables.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic