Question 1002491: A nutritionist recommends that John eat eggs and fish to meet his body's protein and vitamin B requirements. Each ounce of egg contains 40 milligrams of protein and 20 milligrams of vitamin B. Each ounce of fish contains 50 milligrams of protein and 10 milligrams of vitamin B. John needs to reach a target of exactly 580 milligrams of protein and 200 milligrams of vitamin B.
If x and y represent the amounts in ounces of eggs and fish John needs to eat, set the equations of the system.
Express the simpler equation in terms of y.
How many ounces of eggs and fish should John eat?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A nutritionist recommends that John eat eggs and fish to meet his body's protein and vitamin B requirements.
Each ounce of egg contains 40 milligrams of protein and 20 milligrams of vitamin B.
Each ounce of fish contains 50 milligrams of protein and 10 milligrams of vitamin B.
John needs to reach a target of exactly 580 milligrams of protein and 200 milligrams of vitamin B.
If x and y represent the amounts in ounces of eggs and fish John needs to eat, set the equations of the system.
protein eq: 40x + 50y = 580
vitamin b: 20x + 10y = 200
Express the simpler equation in terms of y.
Add the two equations and you get:
60x + 60y = 780
simplify, divide by 60
x + y = 13
x = -y + 13
:
How many ounces of eggs and fish should John eat?
Replace x with (-y+13) in the 1st equation
40(-y+13) + 50y = 580
-40y + 520 + 50y = 580
10y = 580 - 520
10y = 60
10y = 60
y = 60/10
y = 6 oz of fish
then
x = -6 + 13
y = 7 oz of eggs
:
:
Check that out in the original 2nd equation
20(7) + 10(6) =
140 + 60 = 200
|
|
|
