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
Answer this Question please.Thank you im sorry that its so long but I really need help
number of people ---- n
Company A:
CostA = 25n + 50
Company B:
CostB = 20n + 130
So for n = 100
CostA = 2500+50 = 2550
CostB = 2000+130 = 2130
When is CostA = CostB ?
25n + 50 = 20n + 130
5n = 80
n = 16
break-even number is 16 people.
To determine when the two catering companies will cost the same amount of money, let's set up an equation.
Let's use x to represent the number of people who will be eating at the party. Given that the number invited is 100 and includes family members, we can assume that all 100 people will be eating at the party. So, x = 100.
For Catering Company A, the cost can be calculated using the formula:
CostA = $50 (set-up and clean-up fee) + $25 (per person cost) * x
For Catering Company B, the cost can be calculated using the formula:
CostB = $130 (set-up and clean-up fee) + $20 (per person cost) * x
Now, let's set the two equations equal to each other since we want to find when the two companies will cost the same amount:
$50 + $25 * x = $130 + $20 * x
To solve this equation, we can simplify it by combining like terms:
$25 * x - $20 * x = $130 - $50
$5 * x = $80
Now, we can solve for x by dividing both sides by 5:
x = 16
So, the two companies will cost the same amount of money when there are 16 people eating at the party.
To determine which company is the better deal, we can substitute the value of x (16) into both cost equations and compare the total costs.
For Catering Company A:
CostA = $50 + $25 * 16
= $50 + $400
= $450
For Catering Company B:
CostB = $130 + $20 * 16
= $130 + $320
= $450
Both catering companies will cost the same amount, $450, for a party with 16 people. Therefore, either company would be the better deal in terms of cost for you to use.