Answer and Explanation:
Possibly, you forgot to attach the table with the contents of each food. Therefore, I calculated the task with similar values.
1. <em>Assume you have Food A, B, and C. Each has certain amount of Calcium, Iron, and Vit C. </em>
<em> </em>Let's designate: Calcium <em>→ X oz , Iron → Y oz, vit C → Z oz</em>
2. <em>Assume you have following amount of</em><em> Calcium</em><em> in each food: </em>
- Food A = 30 mg/oz
- Food B = 25 mg/oz
- Food C = 20 mg/oz
3. <em>Assume you have following amount of</em><em> Iron </em><em>in each food: </em>
- Food A = 1 mg/oz
- Food B = 1 mg/oz
- Food C = 2 mg/oz
4. <em>Assume you have following amount of</em><em> vit C </em><em>in each food: </em>
- Food A = 2 mg/oz
- Food B = 5 mg/oz
- Food C = 4 mg/oz
<u>Calculations:</u>
→ You have 3 different food and each has Calcium in it. You need exactly 320mg of Calcium per day. Therefore, each food would comprise certain proportion of daily Calcium intake. We can come up with equation: 30X+25Y+20Z = 390 mg
- Similarly, for iron and vitamin C, the next equations could be used:
X+Y+2Z=17 - Iron
2X+5Y+4Z=42 - Vit C
→ Now you have a system of equations:
30X+25Y+20Z = 390 <em>(1) </em>
X+Y+2Z=17 <em>(2)</em>
2X+5Y+4Z=42 <em>(3)</em>
→ Look for similarities! <em>(1) and (3) </em>seem to be similar. We can multiply the <em>(3) </em>by -5 to obtain: -10X-25Y-20Z=-210. We add the <em>(1)</em> and modified <em>(3)</em> equations.
30X+25Y+20Z = 390
-10X-25Y-20Z=-210
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20X+0+0=180
20X=180
<em><u>→ X=9 (oz of Calcium)</u></em>
<em><u></u></em>
→ Now, we can put<em> x=9 </em>into equations above to ease our job:
270+25Y+20Z=390 → 25Y+20Z=390-270=120
9+Y+Z=17 → Y+2Z=17-9=8
18+5Y+4Z=42 → 5Y+4Z=42-18=24
→ Similarly, we can use Eq-s <em>(2) and (3). </em>We can multiply the <em>(2) </em>by -5 to obtain: -5Y-10Z=-40. We add the <em>(3)</em> and modified <em>(2)</em> equations.
-5Y-10Z=-40
5Y+4Z=24
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-6Z=-24
Z=4
<em><u>→ Z=4 (oz of vit C)</u></em>
<em><u></u></em>
→ Now, we can take X+Y+Z=17 <em>(2) </em>and just put in known values(<em>X=9 and Z=4</em>) to obtain Y:
9+Y+4=17
<u>→ Y=17-9-4=4 (oz of Iron)</u>
<u></u>
That's all! So, if you have table values, you can just re-write the equations and doing it stepwise, as it is shown here, you can manage to calculate every value you need :)
