The amount y of red meat consumed per person in the United States (in pounds) in

Question

The amount y of red meat consumed per person in the United States (in pounds) in the
year x can be modeled by the linear equation y ? ?0.3x ?113 . The amount y of all
poultry consumed per person in the United States (in pounds) is the year x can be
modeled by the linear equation y ? x ? 68 . In both models x = 0 represents the year 200.
(Source: Based on data and forecasts from the Economic Research Service, U.S.
Department of Agriculture)
a) What does the slope of each equation tell you about the patterns of red meat and
poultry consumption in the United States?
b) Solve this system of equations. Give the exact values of the solution as well as the
solution rounded to the nearest whole number. In the context of the problem, does it
make sense to give the exact answer or does it make more sense to give the answer
rounded to the nearest whole number? Why or why not?
c) Explain the meaning of your answer from (b).

Explanation / Answer

Since these are linear equations, to find the slope we only have to plug in some value for x, solve for y, twice. (We need two points to find the slope of the line.) So, let x = 5. Red meat = y = 0.3(5) + 113 = 114.5 Poultry = y = (5) + 68 = 73 Then, let x = 10, for point two. Red meat = y = 0.3(10) + 113 = 116 Poultry = y = (10) + 68 = 78 Now we can find the slope of each equation: Red meat line = (116-114.5)/(10-5) = 0.3 Poultry line = (78-73)/(10-5) = 1 This is because slope is (the change in y)/(the change in x). Now the word problems: a) Since both slopes are positive, they tell us that red meat and poultry consumption are both on the rise, but poultry consumption is rising faster than red meat consumption. b) We do this by adding the two equations. We multiply the second equation by -1. This will allow us to eliminate the y's.       y = 0.3 x + 113   + (-y = -x - 68) __________________    0 = -0.7x + 45 -0.7x = -45 x = 64.285714... I'm going to round this to x = 64 and then plug it back in to find y in the first equation. y = 0.3(64)+113 = 132.2 or rounded to 132. So the ordered pair would be (64, 132). Rounding these values would be more effective, since x produces an on-going decimal. c) What the ordered pair implies is that the level of meat consumption (y) is increasing faster than the years (x) are passing, since y > x. Hope this helped! :)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.