3.4 Applying Percents & Problem Solving
Marilyn Nielson
Applications
I need 200 bales of alfalfa to supplement a herd of elk (Cervus elaphus) that winter on my ranch. If I lose 15% of bales to mold, how many do I need to start the winter with?
If a herd of musk oxen (Ovibos moschatus) includes three calves and 15 adult cows, what percent of the herd are calves?
Fourteen percent of streams within the St. Joe watershed support cutthroat trout. If ten streams support cutthroat trout, how many total streams are within the watershed?
Because we approach percent problems differently than percent change problems, we want to make sure that we practice recognizing and solving a variety of percent problems.
So, we have two different formulas for percent problems.
Percent
[latex]\frac{part}{whole} = \frac{percent}{100}[/latex]
Percent change
[latex]\frac{\text{Ending number}}{\text{Starting number}} = \frac{100\pm \text{percent change}}{100}[/latex]
How do we know which one to use?
Terms that indicate time, before/after or increase/decrease may hint that a problem is a percent change situation.
Examples: How Percent and Percent Change are Related
A) About 16% of Idaho fescue seed in this batch is lost because it is not viable and won’t germinate. If I need 2,300 lbs of seed that will germinate to plant later this season – how many pounds should I purchase to start? How many pounds will be lost?
B) An elk loses 22% of his body weight during the fall breeding season (rut). If he weights in at 800 lbs, how much weight will he lose? What weight will he be after the rut?
C) This population of California Quail is growing at a rate of 15% per year. If the population is 350 this year, how many quail will be in the population next year? How many quail will be added?
Can you see the relationship here? A bit?
View the answers.
Watch the solutions video.
Once you’ve squared away which formula to use, you’re most likely to be challenged by the following three common mistakes:
- Getting the Part and Whole reversed on problems where we are looking for the Whole.
- Read the situation carefully. If you are given a number for a segment of a population, like the number of calves, the number of organisms visible, the number of contaminated sites, etc. – you know you’ve got a Part and need to find the Whole.
- Using the incorrect sign on the percent increase or decrease in percent change problems.
- Birth, increase, tax, etc. will use a + sign (100 + percent)
- Mortality, loss, discount, etc. will use a – sign (100 – percent)
- Getting the Starting and Ending numbers reversed on percent change problems where we are looking for the STARTING (base) number.
- Look for clues that the number you are given is the quantity after the percent change has been added or subtracted. Phrases like “we need to end up with”, “mitigation permits require you end with”, “after tax cost”, “at the end of the season”, etc. may be helpful.
Examples: Variety Show
A) If 18% of streams in the St. Joe River watershed are on the 303d list, and 8 streams are on that list – how many total streams are in the watershed?
B) Four Western Toads show limb abnormalities. This represents 22% of the toads captured. How many did we capture?
C) A county in South Carolina has 7.2% sales tax. If I buy 4 rolls of barbed wire at $139. What will the cost be after tax?
D) Young quail have a mortality rate during the first year of life of 85%. If we want to increase the population by 350 adult birds – how many need to be born at the beginning of the season?
E) You’re buying supplies at North 40 and have a 15% off coupon. If you purchase wire stretchers for $40. How much will they cost (before tax) with the coupon? How much will they cost once you’ve added 9% sales tax?
View the answers.
Watch the solutions video.
Problem Set 3.4
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22% percent of streams in the Big Sioux watershed are listed as impaired on the state 404d list. If 12 streams are listed as impaired, how many streams are in the entire watershed?
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I want to increase the population of mallards on my refuge by 275 ducks. If 22% of ducklings released die within the first month, how many ducklings should I release to reach my goal of 275?
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72% of adult rainbow trout stocked in a lake will be caught by anglers and removed from the lake within one year. If I plant 1,250 rainbow trout, how many will be caught?
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72% of adult rainbow trout stocked in a lake will be caught by anglers and removed from the lake within one year. If I plant 1,250 rainbow trout, how many will still be in the lake in one year?
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I need 122 bales of alfalfa to supplement a herd of mule deer that winter on my ranch. If I lose 5% of bales to mold, how many do I need to start the winter with?
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A willow thicket grows by 7% each year. If the thicket included 68 stems this year, how many stems will be present next year?
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If a herd of musk ox includes 7 juvenile oxen and 17 adult oxen, what percent of the herd are juveniles?
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Each year I lose 27% of my willow plantings to beaver. If I want 730 willows on my property at the end of the season, how many do I need to plant at the beginning of the season?
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Our local goose population is growing at a rate of 1.5% per year. If we have 63 geese this year, how many will we have next year?
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If I need 430 fertilizer stakes for this project, and 3% are usually broken or defective in each shipment, how many fertilizer stakes should I order?
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14% of streams within the St. Joe watershed support cutthroat trout. If 23 streams lie within the watershed, how many support cutthroat trout?
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Grazing reduces my population of purple gentian by 4% each year. If I have 127 flowers this season, how many purple gentian will be present next year?
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Every season we lose 5% of our volunteer interns to wild boar attacks. If I need to end this season with 65 working interns, how many should I hire at the beginning of the season?
