Question

todd is planning an graduation party at the house of bratwurst. It costs $150.00 to rent a tent plus $11.50 per person for food. If todd can spend at most $450.00, find the greatest number of people he can invite to the party?

Answer 1

Can you write an expression that shows how much the party costs.
Let y = cost, and x = number of people.
Can you write an expression for y in terms of x?

Answer 2

so for y would that be 450 or would it be 150?

Answer 3

No. I'll explain.
cost = cost of tent + cost for people

Answer 4

cost of tent = 150
So, so far we have y = 150 + cost of people
Ok?

Answer 5

150 + 11.50x = 450
solve for x

Answer 6

ok

Answer 7

The cost for the people is according to this pattern:
For 1 person it costs $11.50
For 2 people is costs 2 * $11.50
For 3 people it costs 3 * $11.50
So,
For x people it costs x * $11.50
Ok?

Answer 8

ok

Answer 9

x * $11.50 can be written as 11.50x

Answer 10

Now we can write the expression for th ecost of the party including the tent and the people:
cost of party = cost of tent + cost of people
y = 150 + 11.50x

Answer 11

ok?

Answer 12

ok

Answer 13

We are told Todd can spend at most $450. The maximum cost he can afford is $450. We let y equal the cost of the party, so we can write:
450 = 150 + 11.50x

Answer 14

ok

Answer 15

Now you solve the equation for x. That gives you the grwatest number of people he can invite to the party. If you get a number with a decimal part, like 23.8, then you have to round down to 23.

Answer 16

got it

Answer 17

great