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**Unformatted text preview: **+ 1250 , 1 t + 250 , t : 0 ≤ t ≤ 2500 }.
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Of what practical use is our answer? Suppose there is only 100 mL of the 90% solution remaining
and it is due to expire. Can we use all of it to make our required solution? We would have y = 100
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so that 2 t + 250 = 100, and we get t = 100 . This means the amount of 30% solution required is
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x = − 3 t + 1250 = − 2 13 + 1250 = 1100 mL, and for the water, w = t = 100 mL. The reader is
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invited to check that mixing these three amounts of our constituent solutions produces the required
40% acid mix.
14 We do this only because we believe students can use all of the practice with fractions they can get! 462 8.1.1 Systems of Equations and Matrices Exercises 1. Put the following systems of linear equations into triangular form and then solve the system if possible. Classify each system as consistent independent, consistent dependent, or
inconsistent. −5x + y = 17 2x − y + z = 1
(a)
2x + 2y − z = 1
x+y = 5
(k) 3x + 6 y + 4 z = 9
x+y+z = 3 2x − y + z = 0
(b)
x − 3y − 4z = 3 −3x + 5...

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