SOLUTION: My assignment was to collect data on 1 cup of broccoli and 1 cup of corn. The amount of calcium in one serving of broccoli is 62.4 mg and 1 mg of iron; in corn there is 5.4 mg of

Question 582012: My assignment was to collect data on 1 cup of broccoli and 1 cup of corn. The amount of calcium in one serving of broccoli is 62.4 mg and 1 mg of iron; in corn there is 5.4 mg of calcium and .6 mg of iron. The RDV for calcium a day is 1000 mg and for iron it is 18 mg. I need to construct and solve a linear system of two equations that would give me the amount of each food that would give me the full recommended values of calcium and iron. Here is the set up for calcium and I ended up with a negative amount:
x + y = 1000
62.4x + 5.4y = 1000
to solve for x x = -y + 1000
62.4(-y + 1000) + 5.4y = 1000
-62.4y + 62400 + 5.4y = 1000
- 62400 = -62400
-62.4y + 5.4y = 61400
-57y = - 61400
y = 1077
x + 1077 = 1000
- 1077 = -1077
x = -77
Can you tell me where I am going wrong?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
My assignment was to collect data on 1 cup of broccoli and 1 cup of corn.
The amount of calcium in one serving of broccoli is 62.4 mg and 1 mg of iron; in corn there is 5.4 mg of calcium and .6 mg of iron.
The RDV for calcium a day is 1000 mg and for iron it is 18 mg.
I need to construct and solve a linear system of two equations that would give me the amount of each food that would give me the full recommended values of calcium and iron
:
x = servings of broc
y = servings of corn
:
Calcium: 62.4x + 5.4y = 1000
:
Iron: 1x + .6y = 18
this equation is easy to arrange for substitution
x = (18-.6y)
:
Replace x with (18-.6y) in the calcium equation
62.4(18-.6y) + 5.4y = 1000
1123.2 - 37.44y + 5.4y = 1000
-32.04y = 1000 - 1123.2
y =
y = +3.845 ~ 4 servings of corn
:
Find x
x = 18 - .6(3.845)
x = 15.692 ~ 16 servings of broc (ugh!)
:
:
See if that checks out for calcium
62.4(16) + 5.4(4) =
998 + 22 = 1020 mg, high because we rounded the servings up
:
You can check the iron requirement
16 + .6(4)
:
I think you went wrong because you did not write an equation for the iron requirement of 18 mg

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