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
If c = 0
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.
