The cost y (in dollars0 to provide food for guests at a dinner party is proportional to the number x of guests attending the party. it costs $30 to provide food for 4 guests. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to provide food for 10 guests? 12? 21?
y=kx
30=k*4
k=7.5
y=7.5 x
a. To write the equation that represents the situation, we need to find the constant of proportionality (k). We are told that the cost of providing food for 4 guests is $30. Since the cost is proportional to the number of guests, we can set up the equation:
y = kx
Replacing y with $30 and x with 4, we get:
30 = k * 4
Solving for k, we divide both sides by 4:
k = 30 / 4
k = 7.5
So the equation representing the situation is:
y = 7.5x
b. The slope of the equation represents the constant of proportionality (k), which tells us how the cost changes with respect to the number of guests. In our equation, the slope is 7.5. This means that for each additional guest, the cost of providing food increases by $7.50.
c. To find the cost of providing food for a certain number of guests, we can substitute the given number of guests (x) into the equation and solve for y (the cost):
For 10 guests:
y = 7.5 * 10
y = 75
So it would cost $75 to provide food for 10 guests.
For 12 guests:
y = 7.5 * 12
y = 90
So it would cost $90 to provide food for 12 guests.
For 21 guests:
y = 7.5 * 21
y = 157.5
So it would cost $157.50 to provide food for 21 guests.