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A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an

order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing
tape, which graph represents how many of each order could be put in a bag hanging from the hook?

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo-example-1
User Bojin Li
by
5.9k points

2 Answers

5 votes

Answer:

Option A.

Explanation:

Let x is the number of orders of paperclips and y is the number of orders of packing tape.

An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.

Total weight =
2x+3y

A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.


2x+3y\leq 6

The related equation is


2x+3y=6

Substitute x=0 in the above equation.


2(0)+3y=6


3y=6


y=2

The y-intercept is 2.

Substitute y=0 in the above equation.


2x+3(0)=6


2x=6


x=3

The x-intercept is 3.

Check the inequality by (0,0).


2(0)+3(0)\leq 6


0\leq 6

This statement is true, it means (0,0) is included in the shaded region.

The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.

Therefore, the correct option is A.

User Chill Web Designs
by
6.5k points
4 votes

Answer:

The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st

Explanation:

* Lets explain how to solve the problem

- The order of jumbo paperclips weighs 2 pounds

- x is the number of orders of paperclips

∴ The weight of the paperclips order is 2 × x = 2x

- The order of packing tape weighs 3 pounds

- y is the number of orders of packing tape

∴ The weight of the tape order is 3 × y = 3y

- The weight of the total order is 2x + 3y

- The hook can hold no more than 6 pounds

∴ 2x + 3y ≤ 6

- Lets find the graph which represent this inequality

∵ The equation of any line is y = mx + c, where m is the slope of the

line and c is the y-intercept

- The y-intercept means substitute x in the equation by 0

- The x- intercept means substitute y in the equation by 0

∵ The inequality is 2x - 3y ≤ 6

∵ The equation of the line is 2x + 3y = 6

- Subtract 2x from both sides

∴ 3y = 6 - 2x

- Divide both sides by 3

∴ y = 6/3 - 2/3 x

∴ y = 2 - 2/3 x

- Find the y-intercept

∵ x = 0

∴ y = 2

∴ The line intersect the y-axis at point (0 , 2)

- Find the x-intercept

∵ y = 0

∴ 0 = 2 - 2/3 x

- Add 2/3 x to both sides

∴ 2/3 x = 2

- Multiply both sides by 3

∴ 2 x = 6 ⇒ divide both sides by 2

∴ x = 3

∴ The line intersect the x-axis at point (3 , 0)

- From the figure the first and the second figures have the same

x-intercept and y-intercept

∵ The inequality is 2x + 3y ≤ 6

- The sign ≤ means the line is sold and the shading is under the line

∴ The first figure is the answer

* The first graph represents how many of each order could be put in a

bag hanging from the hook

User Paul Johnston
by
6.5k points
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