Problem:
- Juanita receives a gift certificate worth 500 pesos from Jollibee Marikina. She wants to buy at most 10 items with this certificate. She likes Yumburger and Jolly Spaghetti. Each Yumburger costs 35 pesos and each Jolly Spaghetti costs 50 pesos. Identify the possible purchase using a graph.
Given:
- Let y be the number of Yumburgers
- Let s be the number of Jolly Spaghetti
Asked:
- Identify the possible purchase using a graph.
Formula/Inequality:
- y + s ≤ 10 and 35y + 50s ≤ 500
Solution:
Solve the inequalities[tex] \tt{.}[/tex]
Given: y + s ≤ 10
If y = 0
- y + s = 10
- 0 + s = 10
- s = 10
If s = 0
- y + s = 10
- y + 0 = 10
- y = 10
Therefore, the ordered pairs are (0,10) and (10,0)
Given: 35y + 50s ≤ 500
If y = 0
- 35y + 50s = 500
- 35(0) + 50s = 500
- 0 + 50s = 500
- 50s = 500
- s = 10
If s = 0
- 35y + 50s = 500
- 35y + 50(0) = 500
- 35y + 0 = 500
- 35y = 500
- y = 14.33
Therefore, the ordered pairs are (0,10) and (14.33,0)
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.
- y + s ≤ 10
- 0 + 0 ≤ 10
- 0 ≤ 10
- TRUE
- 35y + 50s ≤ 500
- 35(0) + 50(0) ≤ 500
- 0 + 0 ≤ 500
- 0 ≤ 500
- 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) Juanita can buy at most 10 pcs of yumburgers or 10 pcs of Jolly Spaghetti.
