Download Solving Proportions

Solving Proportions
MAT222 Intermediate Algebra
Prof Karen Vellekamp
December 13, 2012
SOLVING
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Solving Proportions
When working with rational expression signify fractions, variables, polynomial
fraction, and/or exponents in the numerator and dominator. How we are able to refer to
the problems in this assignment given are through proportions referring to rational
expressions that equal to one another. The cross multiplication of solving proportions is
uncomplicated but when you involve several polynomial terms it can be tricky.
Proportions can be used in various ways of in real life situations. If I am
planning to cook for my children and their friends that total 6 people. I will need 2
pounds of chicken for them. My recipe calls for 2 pounds of chicken for 4 people. Now I
will have to use the proportion equation.
2 = x ; 2(4)= 6(x) ; 8=6x ; 8 = 6x ; 4 = x(←ANSWER)
6 4
6 6
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The problem to work setting ratios with an equation and applicable variable has
this problem to solve. “To estimate the size of the bear population on the Keweenaw
Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a
random sample of 100 bears included only 2 tagged bears. What is the conservationist's
estimate of the size of the bear population?”
50 = 2__
x
100
The proportion on this problem has been set up and we can cross
multiply. The means will be equal to the extremes.
2x = 50(100)
50 and 100 are the extremes in this step. “X” and 2 are the means. I
am now able to divide by 2 on both sides.
2x = 5000
2
2
x= 2500
←The bear population will be a estimate of 2500 bears
SOLVING
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The second problem to solve using proportion equation:
y-1 = - 3
x+3
4
Original Single fraction proportion equation
4(y-1) = -3 (x+3)
Cross multiplying.
4y-4 = -3x-9
Take and distribute 4 on the left and -3 on the right
4y-4+4 = -3x-9+4
Will add 4 to both sides of the problem
4y= -3x -5
4y= - 3x -5
y= - 3x -5
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Divided both sides by 4
4
4
←Answer
There is a second way to solve the equation for problem 10. Would be to take
(x+3) and multiply it by both side of the equation and it will first cancel the denominator
on left and leave only the y-1. Then on the right side we would have -3(x+3)/4. Then can
add the one to both sides y-1+1= 3x/4+3+1.
The coefficient of x is now a negative number when I was a positive in the
original problem.
Reference
SOLVING
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
McGraw-Hill Publishing.
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