(x+4)+(x-3)+(2x+2)+(x^2+3x+1)
1 answer:
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<h3>Answer:</h3>
- <u>20</u> kg of 20%
- <u>80</u> kg of 60%
I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.
That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.
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<em>Using an equation</em>
If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...
... 0.60x + 0.20(100 -x) = 0.52·100
... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20
... x = 32/0.40 = 80 . . . . . kg of 60% alloy
... (100 -80) = 20 . . . . . . . .kg of 20% alloy
So for this polynomial, we will be completing the square. Firstly, what two terms have a product of 20m^2 and a sum of -12m? That would be -10m and -2m. Replace -12m with -2m - 10m:
Next, factor m^2 - 2m and -10m + 20 separately. Make sure that they have the same quantity inside of the parentheses:
Now you can rewrite this expression as . <u>(m - 10) and (m - 2) are your two factors.</u>