Makahanap ng mga eksaktong solusyon sa iyong mga problema gamit ang IDNStudy.com. Ang aming komunidad ay handang magbigay ng malalim at maaasahang mga sagot, anuman ang kahirapan ng iyong mga katanungan.

Solve for problem on system of linear inequities using graphs.

Romeo has 800 pesos. He plans to purchase at least 5 items in the bookstore. He wants to buy coloring books and sets of crayons for his brothers and sisters. Each coloring book costs 100 pesos while a set of crayons is 50 pesos. Determine the possible purchase of the items.​


Sagot :

Problem:

  • Romeo has 800 pesos. He plans to purchase at least 5 items in the bookstore. He wants to buy coloring books and sets of crayons for his brothers and sisters. Each coloring book costs 100 pesos while a set of crayons is 50 pesos. Determine the possible purchase of the items.

Given:

  • Let b the number of coloring books
  • Let c be the set of crayons

Asked:

  • Determine the possible purchase of the items.

Formula/Inequality:

  • b + c ≥ 5 and 100b + 50c ≤ 800

Solution:

Solve the inequalities [tex]\tt{.}[/tex]

Given: b + c ≥ 5

If b = 0

  • b + c = 5
  • 0 + c = 5
  • c = 5

If c = 0

  • b + c = 5
  • b + 0 = 5
  • b = 5

Therefore, the ordered pairs are (0,5) and (5,0)

Given: 100b + 50c ≤ 800

If b = 0

  • 100b + 50c = 800
  • 100(0) + 50c = 800
  • 0 + 50c = 800
  • 50c = 800
  • c = 16

If c = 0

  • 100b + 50c = 800
  • 100b + 50(0) = 800
  • 100b + 0 = 800
  • 100b = 800
  • b = 8

Therefore, the ordered pairs are (0,16) and (8,0)

Plot and connect the points with a solid line since the inequality is ≤. Use (0,0) to identify if the shade is above or below the boundary line.

  • b + c ≥ 5
  • 0 + 0 ≥ 5
  • 0 ≥ 5
  • FALSE

  • 100b + 50c ≤ 800
  • 100(0) + 50(0) ≤ 800
  • 0 + 0 ≤ 800
  • 0 ≤ 800
  • TRUE

Answer:

  • (Attached the photo to see the graph)
  • (with graph) Romeo can buy 5 to 16 sets of crayons or 5 to 8 coloring books.
View image ElaineMorgan12