A caterer charges $158 to cater a party 18 people and $230 for 26 people. Assume that the cost, y, is a linear function of the number of x people. How much would a
party of 42 people cost?

9514 1404 393

  $374

Step-by-step explanation:

For a change of 26 -18 = 8 people, the change in cost is $230 -$158 = $72. The number of people of interest is 42 -26 = 16 more than we know the cost for.

16 = 2 × 8, so we expect the cost for those 16 people to be 2 × $72, or $144.

The cost for 42 people will be $230 +144 = $374.

We could go to the trouble to write an equation for the cost of x people. We know the slope is $72/(8 person) = $9 per person, so we could write the point-slope equation as ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -158 = 9(x -18)

Simplifying to slope-intercept form, this is ...

  y = 9x -162 +158 . . . . eliminate parentheses, add 158

  y = 9x -4

Then for x=42, the cost is ...

  y = 9(42) -4 = 378 -4 = 374 . . . . dollar cost for 42 people