Running head: SOLVING PROPROTIONS
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John Q. Student
MAT 222 Week 1 Assignment
Solving Proportions (title required on first line)
Proportions exist in many real-world applications, such as finding unit price or estimating an
animal population. By comparing data from at least two experiments, conservationists are able to
predict patterns of animal increase or decrease. In this situation, 300 bluegill in Spearhead Lake were
tagged and released to estimate the size of the bluegill population. A month later, after capturing 120
bluegill from the same lake, proportions were used to determine the lake’s population.
This new bluegill scenario can be solved by applying the same concept of proportions used in
the “Capture-Recapture” method in #55 on page 437 (Dugolpolski, 2012). The concept of proportions
allows the assumption the ratio of originally tagged fish to the whole population is equal to the ratio
of recaptured tagged fish to the size of the sample. To determine the estimated solution, variables will
be defined and rules for solving proportions used.
The ratio of originally tagged bluegill to the whole population is 300 /x.
The ratio of recaptured tagged bluegill to the sample size is 45/120.
300 = 45 This is the proportion set up and ready to solve. Cross multiplication is required
120 at this point. The extremes are 120 and 300. The means are x and 45.
120(300) = 45x
36000 = 45x Divide both sides by 45.
x = 800 The bluegill population of Spearhead Lake is estimated to be around 800 fish.
For the second problem in this assignment, the equation must be solved for y. Continuing the
discussion of proportions, a single fraction (ratio) exists on both sides of the equal sign so basically it
is a proportion, which can be solved by cross multiplying the extremes and means.
y + 5 = -1
2(y + 5) = -1(x – 2) The result of the cross multiplying.
2y + 10 = -x + 2 Distribute 2 on the left and -1 on the right.
2y + 10 – 10 = -x + 2 – 10 Subtract 10 from both sides.
2y = -x – 8
2y = -x – 8 Divide both sides by 2
y = -½ x - 4 This is a linear equation in the form of y = mx + b.
After comparing the solution to the original problem, it is noticed that the slope, -½ ,is the
same number on the right side of the equation. This indicates another method exists for solving
y + 5 = -1
y + 5 = -1/2 (x-2)
I would multiply both sides of the equation by (x – 2), which cancels the
y+ 5 -5= -1/2x + 1 -5 denominator on the left, subtract 5 from both sides to get y alone, and
y = -12/x -4
then simplify the right side. It would save a couple of steps from solving it
the other way.
Conclusion paragraph would go here. Remember to include 4-5 sentences to make a
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
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