answers: a. Total fund = 300 x +4000
b. Total Expenses = 3000 + 2500 + 1000 + 2000 + 200 x
c. 300x + 4000 > 200 x + 8500
d.Total Fund : 4000 + 300 x = 3000 + 2500 + 1000 + 2000 + 200 x
Solve for x: 300 x + 4000 = 8500 + 200 x
API: 300 x + 4000 + (-4000) = 8500 + (-4000) + 200 x 300 x = 4500 + 200 x
Transpose: 300x -200 x = 4500 100 x = 4500
MPI : (1/100)100 x=4500 (1/100) 100/100 x=4500/100
x=45
There are 45 attendees.
To check:
4000 + 300 x = 3000 + 2500 + 1000 + 2000 + 200 x 4000 + 300 (45) = 3000 + 2500 + 1000 + 2000 + 200 (45) 4000 + 13500 = 8500+ 9000 17500 =17500
e. 300x+4000>200x+8500
API: 300 x+4000+(-4000 )>200 x+8500+(-4000) 300x>-200x+4500
Transposition: 300x -200x >4500 100x>4500
MPI: (1/100)100 x>4500 (1/100) 100/100 x>4500/100
x>45
The number of minimum attendees are x>45.
f. ? g. ? h. ? i. ? j. ? k. ?
The organization has a budget of 4000 pesos for the event. They expect to earn 300 pesos from the ticket sales per attendee. They need to rent a venue for 3000 pesos. The cost of decorations will be 2500 pesos. Food and beverages are estimated to cost 200 pesos per attendee. The miscellaneous expenses are expected to be 1000 pesos. The food for the volunteers and performers is estimated to cost 2000 pesos. Steps: a. Write the linear equation to represent the total fund based on the number of attendees. Let x be the number of attendees. b. Write a linear equation to represent the total expenses based on the number of attendees. c. The organization plans to return the budget of 4000 pesos to the organization's reserve fund. Hence, the total income from the tickets should cover all the expenses. Write an inequality to represent the condition that the total income should be greater than the total expenses. d. Setup an equation to determine the breakeven point (where total sales equals total expenses). Solve for x. e. Calculate the minimum number of attendees required for the event to be profitable. Solve for the inequality in Step C. f. The organization aims to earn at least 15000 pesos. The earnings will be used to fund their upcoming projects. How many tickets should they be able to sell to achieve their target profit? g. The group plans to sell t-shirts during the concert. The cost of the shirt and printing is 175 pesos per shirt. They plan to sell the shirt for 350 pesos. The profit from the shirts will be used to purchase school supplies for the students. How many t-shirts should they sell if the estimated cost of the school supplies is 12000 pesos. h. Let y be the total income from the tickets. Write the linear equation in two variables to represent the total income. Complete the table below. Plot the points on the Cartesian plane and connect the points to form the graph. Let be the y the total expenses. Write the linear equation in two variables to represent the total expenses. Complete the table below. Plot the points on the Cartesian plane and connect the points to form the graph. What does the graph tell you about the relationship between income, expenses, and the break-even point? Based on your analysis, make recommendations to organization regarding the number of attendees needed to stay within budget and make a profit. Provide a brief summary of your budget plan and the key factors the organization should consider for the event. The organization has a budget of 4000 pesos for the event. They expect to earn 300 pesos from the ticket sales per attendee. They need to rent a venue for 3000 pesos. The cost of decorations will be 2500 pesos. Food and beverages are estimated to cost 200 pesos per attendee. The miscellaneous expenses are expected to be 1000 pesos. The food for the volunteers and performers is estimated to cost 2000 pesos. Steps: a. Write the linear equation to represent the total fund based on the number of attendees. Let x be the number of attendees. b. Write a linear equation to represent the total expenses based on the number of attendees. c. The organization plans to return the budget of 4000 pesos to the organization's reserve fund. Hence, the total income from the tickets should cover all the expenses. Write an inequality to represent the condition that the total income should be greater than the total expenses. d. Setup an equation to determine the breakeven point (where total sales equals total expenses). Solve for x. e. Calculate the minimum number of attendees required for the event to be profitable. Solve for the inequality in Step C. f. The organization aims to earn at least 15000 pesos. The earnings will be used to fund their upcoming projects. How many tickets should they be able to sell to achieve their target profit? g. The group plans to sell t-shirts during the concert. The cost of the shirt and printing is 175 pesos per shirt. They plan to sell the shirt for 350 pesos. The profit from the shirts will be used to purchase school supplies for the students. How many t-shirts should they sell if the estimated cost of the school supplies is 12000 pesos. h. Let y be the total income from the tickets. Write the linear equation in two variables to represent the total income. Complete the table below. Plot the points on the Cartesian plane and connect the points to form the graph. Let be the y the total expenses. Write the linear equation in two variables to represent the total expenses. Complete the table below. Plot the points on the Cartesian plane and connect the points to form the graph. What does the graph tell you about the relationship between income, expenses, and the break-even point? Based on your analysis, make recommendations to organization regarding the number of attendees needed to stay within budget and make a profit. Provide a brief summary of your budget plan and the key factors the organization should consider for the event
