Problem:
- Mamerta has saved 200 pesos from her allowance. Her sister will have her birthday next week. She wants to buy candies and chocolates to make loot bags. There will be at most 10 guests in the party. Each set of candies costs 8 pesos while a set of chocolates costs 10 pesos. Will each of the guests have a loot bag? Justify your answer.
Given:
- Let c be the set of candies
- Let h be the set of chocolates
Asked:
- Will each of the guests have a loot bag?
Formula/Inequality:
- c + h ≤ 10 and 8c + 10h ≤ 200
Solution:
Solve the inequalities.
Given: c + h ≤ 10
If c = 0
- c + h = 10
- 0 + h = 10
- h = 10
If h = 0
- c + h = 10
- c + 0 = 10
- c = 10
Therefore, the ordered pairs are (0,10) and (10,0)
If c = 0
- 8c + 10h = 200
- 8(0) + 10h = 200
- 0 + 10h = 200
- 10h = 200
- h = 20
If h = 0
- 8c + 10 = 200
- 8c + 10(0) = 200
- 8c + 0 = 200
- 8c = 200
- c = 25
Therefore, the ordered pairs are (0,20) and 25,0)
Plot and connect the points with a solid line since the inequality is ≤. Use (0,0) to identify if the shade part is above or below the boundary line[tex] \tt{.}[/tex]
- c + h ≤ 10
- 0 + 0 ≤ 10
- 0 ≤ 10
- TRUE
- 8c + 10h ≤ 200
- 5(0) + 10(0) ≤ 200
- 0 + 0 ≤ 200
- 0 ≤ 200
- TRUE
Since both inequalities are TRUE statement, then the shaded part is below the boundary line.
- (Attached the photo to see the graph)
Answer:
- (with graph) Each of the guests will have a loot bag.
