Giselle has a catering business. There is a proportionalrelationship between the number of people and theamount of meat she uses for an event. The graph showsthe amount of meat Giselle uses for 10 people. Find theamount of meat needed for 20, 30, 40, and 50 people.Finish labeling the graph and plotting ordered pairs.Finally, explain how to calculate the amount of meatneeded for a party of 75 people.
Accepted Solution
A:
Answer: 1) The graph labeled and the ordered pairs plotted are shown in the second picture. 2) To calculate the amount of meat (in pounds) needed for a party of 75 people: Substitute the value of the Constant of proportionality and [tex]x=75[/tex] into the equation [tex]y=kx[/tex] and then evaluate (The result is 30 pounds).Step-by-step explanation: The missing graph is attached. Proportional relationships have the following form: [tex]y=kx[/tex] Where "k" is the Constant of proportionality. 1) You can observe in the graph shown in the first picture this point: [tex](10,4)[/tex] So you can subsitute the coordinates of this point into [tex]y=kx[/tex] and solve for "k": [tex]4=k(10)\\\\k=\frac{4}{10}\\\\k=\frac{2}{5}[/tex] Now you can find the amount of meat needed for 20, 30, 40, and 50 people with this procedure: For 20 people Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=20[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get: [tex]y=(\frac{2}{5})(20)=8[/tex] The ordered pair is: [tex](20,8)[/tex] For 30 people Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=30[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get: [tex]y=(\frac{2}{5})(30)=12[/tex] The ordered pair is: [tex](30,12)[/tex] For 40 people Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=40[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get: [tex]y=(\frac{2}{5})(40)=16[/tex] The ordered pair is: [tex](40,16)[/tex] For 50 people Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=50[/tex] into the equation [tex]y=kx[/tex] and evaluating, you get: [tex]y=(\frac{2}{5})(50)=20[/tex] The ordered pair is: [tex](50,20)[/tex] Knowing those values of "y"and having the ordered pairs, you can finish labeling the graph an plotting the ordered pairs (See the second picture.). 2) Substituting [tex]k=\frac{2}{5}[/tex] and [tex]x=75[/tex] into the equation [tex]y=kx[/tex] and evaluating, you can calculate the amount of meat (in pounds) needed for a party of 75 people. This is: [tex]y=(\frac{2}{5})(75)=30[/tex]