So i have this project and i need help on it.
It says ....As your 8th grade graduation approaches,your parents decide to begin planning for your graduation party.Your parents have asked for your help in deciding which companies will be the better deal for them to use since you are better in math then they are.
Task 1:Determine how many people you are going to invite to your graduation party (remember to include family members)Number Invited:100(my class picked 100 for the people invited)
Task 2:Decide which catering company is the better deal for the amount of people you are inviting.
(catering Company A charges a fee of $50 for set-up and clean-up plus an additional $25.00 per person that will be eating at the party.Catering Company B charges a fee of $130 for set-up and clean-up plus and additional $20 per person that will be eating at the party.
HERE IS THE QUESTION : When will the two companies cost the same amount of money? set up an equation and solve to prove your answer.
Another question:Which company is the better deal for you to use? show your work
For x people, we have
A: 50+25x
B: 130+20x
So, you want
50+25x = 130+20x
To solve the first question, let's set up an equation:
Let's assume x represents the number of people attending the party.
For Catering Company A, the cost will be $50 (set-up and clean-up fee) + $25 (per person) * x (number of people). This can be written as:
Cost A = $50 + $25x
For Catering Company B, the cost will be $130 (set-up and clean-up fee) + $20 (per person) * x (number of people). This can be written as:
Cost B = $130 + $20x
To find when the two companies cost the same, we can set up an equation:
$50 + $25x = $130 + $20x
Now let's solve the equation to find the value of x:
$25x - $20x = $130 - $50
$5x = $80
x = $80/$5
x = 16
Therefore, the two companies will cost the same amount when 16 people are attending the party.
To answer the second question, we need to compare the costs of the two companies for different numbers of people attending the party.
For example, let's find the costs for 20 people:
Cost A = $50 + $25 * 20 = $50 + $500 = $550
Cost B = $130 + $20 * 20 = $130 + $400 = $530
From this calculation, we can see that for 20 people, Company B is the better deal as it costs $530 compared to Company A's cost of $550.
By performing similar calculations for different numbers of people, you can determine which company is the better deal for various scenarios.