Thread: review of algebra 2

Hi, I really need some help on these 3 problems of my algebra 2 review.
They are:

1. Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year, If she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?

2. How many cubic centimeters of pure hydrochloric acid should be added to 20cc of a 30% solution of hydrochloric acid to obtain a 50% solution?

3. The line x-2y=-4 is tangent to a circle at (0,2). The line y=2x-7 is tangent to the same circle at (3,-1). Find the center of the circle.

Thanks for your help.

Four postings that have exactly the same contents--3 problems!

Better, or preferable is one posting with only one problem.

So, since there are 3 problems here, I will not give detailed answers as I used to. I might run out of space/window on my monitor here.

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1. Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year, If she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?

Let x = part of the $1,000,000 that she can lend at 16%

0.16(x) +0.19(1,000,000 -x) = 0.18(1,000,000) -----***
x = (180,000 -190,000) / (0.16 -0.19)
x = $333,333.00 -------answer.

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2. How many cubic centimeters of pure hydrochloric acid should be added to 20cc of a 30% solution of hydrochloric acid to obtain a 50% solution?

Pure acid is 100% concentration.
Let x = cc of pure acid to be added.

1.00(x) +0.30(20) = 0.50(x+20)
x = (0.50*20 -0.30*20) / (1.00 -0.50)
x = 8 cc ---------answer.

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3. The line x-2y=-4 is tangent to a circle at (0,2). The line y=2x-7 is tangent to the same circle at (3,-1). Find the center of the circle.

The center is radius away from tangent points (0,2) and (3,-1).
Let (x,y) = center

distance = sqrt[(x2 -x1)^2 +(y2 -y1)^2]

radius = radius
sqrt[(x-0)^2 +(y-2)^2] = sqrt[(x-3)^2 +(y- (-1))^2]
Square both sides,
x^2 +(y-2)^2 = (x-3)^2 +(y+1)^2
.....
Umm, are you sure the problem as posted is complete? No lacking information? The radius of the circle is not given?

Sorry about that, i really needed the answer, but thanks. Next time i'll post more conservatiely.