SOLUTION: ``Your mother wants grapes and bananas for her fruit salad. You found out that grapes sells at Php 200 per kilogram and the banana sells at Php150 per kilogram. How many possible

Question 1174174: ``Your mother wants grapes and bananas for her fruit salad. You found out that grapes sells at Php 200 per kilogram and the banana sells at Php150 per kilogram. How many possible kilogram of each item, you will buy if the total cost is not to exceed Php 500?
Requirement for the Presentation of the Problem.
1. Representation of the given. (Ex. Let x be the no. of apple)
2. Systems of Linear Inequalities
3. Graph of the System of Linear Inequalities
4. Name two solutions of the system.
.

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Absolutely! Let's solve this problem step by step.
**1. Representation of the Given**
* Let **x** be the number of kilograms of grapes.
* Let **y** be the number of kilograms of bananas.
* Price of grapes: Php 200 per kilogram
* Price of bananas: Php 150 per kilogram
* Total budget: Php 500
**2. Systems of Linear Inequalities**
* **Cost Inequality:** The total cost of grapes and bananas must not exceed Php 500.
* 200x + 150y ≤ 500
* **Non-negativity Constraints:** You cannot buy negative kilograms of fruit.
* x ≥ 0
* y ≥ 0
**3. Graph of the System of Linear Inequalities**
* **Simplify the Cost Inequality:**
* 200x + 150y ≤ 500
* Divide by 50: 4x + 3y ≤ 10
* **Find the Intercepts of 4x + 3y = 10:**
* If x = 0, then 3y = 10, so y = 10/3 ≈ 3.33
* If y = 0, then 4x = 10, so x = 10/4 = 2.5
* **Graph the Line:** Plot the points (0, 3.33) and (2.5, 0) and draw a line connecting them.
* **Shade the Region:** Since 4x + 3y ≤ 10, shade the region below the line.
* **Graph the Non-negativity Constraints:** Shade the region where x ≥ 0 (right of the y-axis) and y ≥ 0 (above the x-axis).
* **Feasible Region:** The feasible region is the area where all inequalities overlap. This will be a triangle in the first quadrant, bounded by the x-axis, y-axis, and the line 4x + 3y = 10.
**4. Name Two Solutions of the System**
* **Solution 1:**
* x = 1 kg of grapes
* y = 2 kg of bananas
* Cost: (200 * 1) + (150 * 2) = 200 + 300 = Php 500 (within the budget)
* This point (1,2) is within the feasible region.
* **Solution 2:**
* x = 0.5 kg of grapes
* y = 2 kg of bananas
* Cost: (200 * 0.5) + (150 * 2) = 100 + 300 = Php 400 (within the budget)
* This point (0.5,2) is within the feasible region.

RELATED QUESTIONS
Your mother wants grapes and bananas for her fruit salad. You found out that grapes... (answered by Alan3354)

Your mother wants grapes and bananas for her fruit salad. You found out that grapes... (answered by CubeyThePenguin,ikleyn)

I am having trouble setting up this word problem: A fruit salad contains an equal number... (answered by jorel1380)

Grapes sell for $4.24 per kilogram. How much do these grapes sell for per... (answered by Alan3354)

Michelle, a product buyer for t and c market purchased 500 pounds of grapes for .39 cents (answered by josgarithmetic)

You are a caterer and you need to make a 22.5 pound fruit salad. The ratio is 2 parts... (answered by stanbon,g6qwerty)

If grapes cost .93 per pound and I buy .74 pounds, how much will I pay for the... (answered by Alan3354)

Beth is making fruit salad. She adds 3 grapes for every 2 strawberries. If she uses 20... (answered by Cromlix)

Mr. Charles bought a total of 5 pounds of fruit. He spent $6.58 and he bought apples,... (answered by ikleyn,macston)