a) solve for r : s=p(1+rt)  b) y(9/1 + 0.625 x 254/365) + (1 - 0.875 x 116/365) - round all your coefficents to 4 decimal places  c) x(1.04)^4 + $195 + (x/1.04^3) = $405/1.04^2 $ -- solve...

a) solve for r : s=p(1+rt) 

b) y(9/1 + 0.625 x 254/365) + (1 - 0.875 x 116/365) - round all your coefficents to 4 decimal places 

c) x(1.04)^4 + $195 + (x/1.04^3) = $405/1.04^2 $ -- solve equattion to nearest cent

Asked on by malikmj

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steveschoen | College Teacher | (Level 1) Associate Educator

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a) To solve for r, there are several ways.  One way would be to first divide each side by p.  So:

s=p(1+rt)

s/p = 1+rt

Then, we can subtract 1 from each side

s/p - 1 = rt

Then, divide by t

(s/p - 1)/t = r

b)

To solve this problem, we sue the order of operations, or PEMDAS.  Or:

1) parenthesis

2) exponents

3) multiplication and division left to right

4) addition and subtraction left to right

Probably biggest thing with this is an example like:

9-3+4

Students get use to doing the addition first.  But, addition and subtraction are all done at the same time.  When there are several of them to do, we are suppose to start left to right.  So, we do subtraction first, 9-3 = 6.  Then, we add 4 for 10.

Back to our problem:

y = (9/1 + 0.625 x 254/365) + (1 - 0.875 x 116/365)

So, we do what's inside the parenthesis first.  in the first one, we still have division, addition, multiplication, and division to do.  So, we do the multiplication and division first, left to right.  So:

y = (9 + 158.75/365) + (1 - 0.875 x 116/365)

y = (9 + 0.4349315) + (1 - 0.875 x 116/365)

y = (9.4349315) + (1 - 0.875 x 116/365)

For the second parenthesis, we have subtraction, multiplication, and division.  So, we do the multiplication and division first:

y = (9.4349315) + (1 - 101.5/365)

y = (9.4349315) + (1 - 0.27808219)

y = (9.4349315) + (0.721917808)

So, adding these together and rounding to 4 places:


10.1568

c) To solve this, there are several ways.  We could first simplify all terms.  So:

x(1.04)^4 + $195 + (x/1.04^3) = $405/1.04^2

1.1698585x + 195 + 0.888996359x = 374.44526627

I will look to carry out all my decimals, rounding at the end.

So, then, add like terms on the left side:

2.05885491867x + 195 = 374.44526627

Then, we subtract 195 from each side:

2.05885491867x = 179.445266272

Dividing each side by 2.05885491867, rounding to the nearest cent:

x = 87.16

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