Mathematics ReviewToday:•Ratios•Proportions•More Word Problems

Be prepared!Today and next week, most of the problems

will be Word Problems

RatiosRatios are a way of comparing 2 or more things.We use ratios ALL THE TIME.Mpg is a ratio, it relates MILES to the number of GALLONSI could list the uses of ratios in every day life, but we really don’t have the time. They are in EVERY industry, EVERY job.Gas at $3.49, that is $3.49 for 1 gallon, or PER gallon

ProportionsWhen 2 or more ratios are equal than they are proportional.Proportions deal with 2 (or more things) that change, but change at the same rate (as 1 gets bigger, the others do, and vice versa)Proportions can be quite confusing, mostly because they can be phrased in many different ways, and without careful consideration, might appear to be different types of problems.To solve proportions we basically are just converting fractions to other equivalent fractions

BE CAREFUL!If 5 people eat 4 steaks;How many steaks do 15 people eat?How many people would eat 24 steaks?

If it takes 5 people 4 hours to eat a bunch of food;How long would it take 8 people to eat the same bunch?How many people would you need if you only had 2 hours?

Both of these problems deal with 2 things, people and food. What is the difference?

They’re Everywhere!Proportions are dealing with things that are “part of the whole”. If 1 apple costs $5 how much do 4 apples cost? That is a proportion, true, easy, but still a proportion.

Be careful with TimeTime is a very weird thing, and DOES NOT WORK like everything else.

There is a 2 mile straight line race track. If you go 30mph the first mile of the track, how fast do you have to go the second mile to average 60mph for the whole 2 miles?

A hen and a half, lays an egg and a half, in a day and a half, how long will it take 10 hens to lay 10 eggs?1.5 hens lay 1.5 eggs in 1.5 days.

Unit “Price”Unit price we use all the time. It is a ratio. In most cases you are dealing with the price of a single unit, but it can easily be applied to things that are not using dollars, or prices.A unit price is the ‘cost’ per single unit, thus it is the numerator when the denominator is 1.It usually will be a decimal.The unit price is the decimal value of the fractions numbers, while the unit will still be the top unit divided by bottom.

Unit ConversionTo show you the use of proportions and ratios. This may not be that much use to you directly.

For example. You need 90 square feet of material, but it is only available by the square yard. How many square yards do you need?

You are in Europe, and you are going 65mph when you see a sign that says that the speed limit is 110km per hour. Are you speeding? (1.6km=1mi)

What if, god forbid, the sign said that the speed limit was 2 kilometers per minute. Are you speeding now?

Ratios w/>2Sometimes a recipe calls for mixing this part of 1, with this part of another, with this part of a third, many times cocktails are like this.Not a big drinker, but lets say we have this drink;1 part vodka to 2 parts rum to 3 parts coke.That is for 1 drink, how much of each would you need for 5 drinks?What about if you wanted to make 12 liters to bring to a picnic, how much of each do you mix?

PHLEXGLOBAL MATH QUIZ

There are 211 documents in a file – 40 of these are 1572’s, 74 of these are Investigator CV’s, 45 of these are Ethics approvals and 52 are CRFs.  An auditor wants to examine a sample of 75 of the documents in the file, but the 75 documents have to be spread across each document type in the same proportion as the overall file contents.  Therefore, how many Investigator CV’s does the auditor examine? 

A project consists of scanning the contents of 226 boxes.  Eight scanners (A – H) are used for this work.  Each scanner completed the following number of boxes:

If the project is budgeted $200,000, how much does scanner D make, proportionally?

Write an equation, and solve it for the following problem; Michael and Jane are ordering packages of material. If Jane orders 6 more than half as many as Michael orders, how many do each order if a total of 33 packages have been ordered?

Write an equation, and solve it for the following problem; Sarah and Isiah are each prepping files of documents.  If the total number of files prepped is 95, and if Sarah has prepped 35 more than a third of what Isiah has prepped, how many files has each person prepped?

We need to QC an average (mean) of 40 boxes per day over a two week period (10 working days).  In the first nine days, we QC’d the following number of boxes: 35, 42, 50, 19, 21, 39, 46, 47 and 49.  How many boxes do we need to QC on the 10th working day in order to achieve the average of 40 boxes per day.

If we know that our profit from the equation;Profit=(x-8)*400+900, with x being the number of items we have sold, how many items do we need to sell if we want a profit of $16900?

Phlexglobal charges $1.50 per page processed. There are 5 steps involved in processing a page:

Goods Receiving – takes an average of 5 seconds per page

Prepping – takes an average of 40 seconds per pageScanning – takes an average of 20 seconds per pageQuality Checks – takes an average of 15 seconds per

pageFiling – takes an average of 10 seconds per page

The revenue per page is allocated across these 5 steps based on time taken.

• How much of the revenue should be allocated to the prepping process?

• How many pages should be scanned by a team member in order for that team member to achieve a target daily rate of $250

A new project is estimated to take 30 people 20 full days to finish. Unfortunately when the project starts only 25 people were available. How many days should it take the 25 people to finish the same project?

If a large client is given a discount of 15% off their order, and the cost AFTER discount comes to $12750, what was the original cost of the order, if the client did not have the discount?

If each binder has an average of 387 pages, and each box has an average of 14 binder, and each carton has 6 boxes, and each pallet has an average of 16 cartons on it, how many pages should one expect to have in 7 pallets?