Question

A restaurant is holding an all you can eat ribs event. the initial serving of the meal includes half a slab of ribs, a loaded baked potato, roasted garlic green beans, and a 750 mL soft drink. A customer can order as many additional quarter slabs of ribs as they want at no additional cost. The following information shows the number of calories in each menu item:

Half slab of ribs: 613
Quarter slab of ribs: 328
Loaded baked potato: 532
Roasted garlic green beans: 298
750 mL soft drink: 295
a) Suppose a person ate the entire meal, but did not order any additional ribs. How many calories did that person consume?
b) Let C represent the number of calories consumed, and let Q represent the number of additional quarter slabs of ribs ordered. Write a linear equation relating C and Q.
c) Sketch a graph of the related linear equation.
d) what do the slope and C-intercept represent in this scenario?
e) The Canadian food guide suggests that a 16 year old male with a sedentary lifestyle should consume about 2300 calories per day. Use the linear equation to determine the number of additional quarter slabs a 16-year-old male could eat and still stay below the daily recommendation (assuming the male does not eat anything else that day)
f) use the recommended caloric intake to state the domain and range of the relation from part e

Answer 1

Well for part a all you have to do is add all of the intial calories toghther except for the quarter slab of ribs as for it isnt included in the intial meal
613+532+298+295= 1738 calories

for part b you do a simple y=mx+b equation (C=y and Q=x 1738=b)

C = 328Q + 1738

Plug that equation into a calculator to find a graph and sketch

The slope represents the amount of calories you add onto your initial amount of calories (1738), and the C-intercept represents your starting amount of calories from the original meal

For part E just use your graphing calculator to see where your linear equation is equal to 23 and use the X value at that point as the amount of Quarter slabs the teenager could ingest, assuming you do not have a calculator, the answer is around 2 quarter slabs

The domain and range at that point is (2,2394)