SOLUTION: Determine how much of each food item you need in order to reach DV levels. Construct and solve a linear system of two equations that would make that determination. THE DV OF CALCIU

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Question 743755: Determine how much of each food item you need in order to reach DV levels. Construct and solve a linear system of two equations that would make that determination. THE DV OF CALCIUM IS 1000 mg AND DV OF IRON IS 18 mg
The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli CALCIUM = 159 mg / IRON 2.04 mg
The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn
CALCIUM = 9.09 mg /IRON = 0.95 mg
HOW DO I EVEN BEGIN TO WRITE THIS? LET ALONE SOLVE IT? THANK YOU FOR ANY HELP!
Answer by davethejackal(28) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = half cups corn you eat.
Let b = packets broccoli you eat

So if you are eating just corn and broccoli, the amount of calcium you will take in is:
9.09 mg / half cup corn + 159 mp / pack broccoli)
= 9.09c + 159b | [1]
The amount of calcium you need is 1000 mg
So, using [1] we get 9.09c + 159b = 1000 | [3]

Similarly the amount of iron you get from eating the two foods is given by
2.04 mg / pack broccoli + 0.95 / half cup of corn
= 2.04b + 0.95c | [2]

The amount of iron we need is 18mg
Hence from [2] we get 18 = 2.04b + 0.95c | [4]

Rearranging [3] gives
+b+=+%281000+-+9.09c%29%2F159+ | [5]

Substituting for b in [4] gives
+2.04%281000+-+9.09c%29%2F159+%2B0.95c+=+18+

+2.04%281000%29%2F159+-+2.04%289.09c%29%2F159+%2B+0.95c+=+18+

+%280.95+-+2.04%289.09%29%2F159%29c+=+18+-+2.04%281000%29%2F159+

+c+=+%2818+-+2.04%2A%281000%29%2F159%29%2F%280.95+-+2.04%2A%289.09%29%2F159%29+
Hence c= 6.20 half cups of corn (or 3.10 cups corn) to 2 dp

Substituting for c in [5] gives:
+b+=+%281000+-+9.09c%29%2F159+=+%281000-9.09%2A%286.20%29%29%2F159+
= 5.93 bags of broccoli.
= 59.3 oz broccoli since there are 10 oz per bag.

Testing in original statements:

" in one 10 oz package of broccoli CALCIUM = 159 mg / IRON 2.04 mg"
Hence with 5.93 bags we have 159 x 5.93 g calcium = 942.87 g
And 5.93 x 2.04 g iron = 12.10g (to 2 d.p.)

"in a ½ cup of frozen corn CALCIUM = 9.09 mg /IRON = 0.95 mg "
Hence in 6.2 half cups we get 9.09 x 6.2 g calcium = 56.36g (to 2 d.p)
and we get 0.95 x 6.2 = 5.89g iron

Total amount of iron = 12.10+5.89 = 17.99 = 18.0 to 1 dp.
Total amount of calcium = 942.87 + 56.36 = 999.23 QED (http://en.wikipedia.org/wiki/Q.E.D.)

That's a lot of broccoli!