Combine 5x and x and that makes 6x+3
To finish in 5 weeks:
For 4 of those weeks, read 4 chapters per week. On one of the weeks read 3 chapters.
To finish in 4 weeks:
For 3 of those weeks, read 5 chapters per week. On one of the weeks read 4 chapters.
To finish in 3 weeks:
For 2 of those weeks, read 6 chapters per week. On one of the weeks read 7 chapters.
To finish in 2 weeks:
On one week read 10 chapters. On the other week read 9 chapters.
To finish in 7 days:
For 6 of those days, read 3 chapters. On one of the days, read 1 chapter.
Answer: 8n
Let's simplify step-by-step.
(2(n+1)−1)2−(2n−1)2
Distribute:
=4n2+4n+1+−4n2+4n+−1
Combine Like Terms:
=4n2+4n+1+−4n2+4n+−1
=(4n2+−4n2)+(4n+4n)+(1+−1)
=8n
Suppose x grams of 8% solution should be mixed to make 100 g of 3% solution.
here we shall have:
the amount of 3% solution in the 100 g will be:
3/100*100=3 grams
the the equation will be, 8% of what quantity becomes 3g?
(8/100)*x=3
hence solving for x we shall have:
0.08x=3
x=3/0.08
x= 37.8 grams
The implication of this is that, when you have 37.5 grams of 8% solution, that will contain 3 of pure chemical and hence when you add more solvent on top of 37.5 g until you reach 100g, that will be 3% solution.
A graphing calculator can do a linear regression on these points very easily. The y-intercept is 107.
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If you want to do this by hand, you can use the 2-point form of the equation for a line, then evaluate for x=0.
.. y = (100 -102)/(35 -25)*(x -25) +102
.. y =-2/10*(0 -25) +102
.. y = 107
