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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