Mr and mrs waugh want to use a caterer for a birthday party for their twin sons. the manager says the cost for a family of four would be $160. however, the sons want to invite 8 friends, making 12 people in total. the cost for this would be $360. if the total cost in each case is made up of the same cost per person and the same fixed cost, find the cost per person and the fixed cost.

$60 fixed price        $25 per person

Step-by-step explanation:

x=price per person

c= fixed cost

4x+c =160

12x+c=360

I will multiply the first by -1:

-4x -c=-160

12x+c=360

ADD BOTH:

8x     = 200

x=25  ($25 per person)

25*4=100

160-100 = 60 (fixed cost =60)

25*12=300

300 + 60(fixed cost) = 360

1; 35 is the ratio

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.