The cost y (in dollars) 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?
a) Y = 7.5x
b) slope = 7.5 = cost per guest
c) 7.5(10) = $75
a. To write an equation that represents the situation, we can start by noting that the cost y is proportional to the number x of guests attending the party. This means that the relationship between the variables can be expressed using a constant of proportionality, which we'll call k.
Given that it costs $30 to provide food for 4 guests, we can set up a proportion to find the constant of proportionality:
30/4 = k
Simplifying the left side of the equation, we have:
7.5 = k
Thus, the equation representing the situation is:
y = 7.5x
b. The slope of the equation, 7.5, represents the cost per guest. It tells us that for every additional guest, the cost of providing food increases by $7.5. In other words, the slope represents the rate of change in the cost with respect to the number of guests.
c. To find out how much it costs to provide food for 10 guests, we can use the equation we derived in part a:
y = 7.5x
Plugging in x = 10, we have:
y = 7.5 * 10 = 75
Therefore, it would cost $75 to provide food for 10 guests.