MATH SOLVE

4 months ago

Q:
# A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and anorder of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packingtape, which graph represents how many of each order could be put in a bag hanging from the hook?

Accepted Solution

A:

Answer:The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1stStep-by-step 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