Math 6H ( Periods 3, 6, & 7)

Ratio 7-6 Word Problems
Since all of the word problems from Ratios 7-6 are excellent examples of using Ratios, I thought I would create a blog posting with the solutions. We did all of the even numbered ones in class and went over the answers to the odd numbered ones—as they were assigned for homework. Although I will list the actually word problems, you might need to turn to the textbook and page 229 for any charts included.
Read each problem carefully and set up the solutions based on the question asked
Page 229
1. What is the cost of grapes in dollars per kilogram if 4.5 kg of grapes costs $ 7.56?
Since they want $/kg you need to have 7.56/ 4.5 = 1.68; so the grapes cost $ 1.68/kg.

2. This one looked confusing, but just read it a few times: The index of refraction of a transparent substance is the ratio of the speed of light in space to the speed of light in the substance. (Read it again—it is just a ratio). Using the table on Page 229, find the index of refraction of
A. Glass
B. Water

According to the table Speed of light in space is 300,000 km/sec
Speed of light in glass is 200,000 km/ sec.
So
300,000
200,000
or 3/2

Speed of Light in Water is 225,000

so that ratio is
300,000
225,000
This takes a little more time dividing but you can simplify it to 4/3 Since it is a ratio you want to LEAVE it as an improper fraction.


3. The mechanical advantage of a simple machine is the ratio of the weight lifted by the machine to the force necessary to lift it. Now—just read that again—you don’t need to truly understand physics to get this problem. It is a RATIO again!! What is the mechanical advantage of a jack that lifts a 3200-pound car with a force of 120 pounds?

3200 =
120
80/3; so the mechanical advantage is 80/3

4. The C-String of a cello vibrates 654 times in 5 seconds, How many vibrations per second is that? (We are finding unit rate)
It’s a rate of time/sec.
654/ 5 = 130 4/5 vibrations per second

5. A four cubic foot volume of water at sea level weighs 250 lb. What is the density of water in pounds per cubic foot? (Do you need to understand density to do this problem?) No—just unit rates!! We want lbs/cubic foot. Look at the information and place it with lbs/ft and then divide to get the unit rate.
250lb/ 4 ft³. That equals 62 1/2 lb/ft³ .

6. A share of stock that costs $88 earned $16 last year. What was the price-to-earnings ratio of this stock? (Wish that was happening now!!)
Price/earnings so look carefully 88/16 = 11/2 so the Ratio is 11/2

In exercises 7 and 8 you will need to look at the diagrams on page 230. You are finding the ratio in lowest terms.
Look at both the small and large triangles. For A you are finding the ratio between segment AB of the larger triangle and DE of the smaller triangle.
4.8
3.2
Simplify ( I like to clear decimals to make it easier but in this case you could easily divide
= 3/2
B.
Perimeter of Triangle ABC
Perimeter of Triangle DEF

First you need to find the perimeter of the larger triangle by adding up the three sides
6.3 + 4.8 + 3 = 14.1
and then finding the perimeter of the smaller triangle by adding up those three sides
4.2 + 3.2 + 2 = 9.4

14.1
9.4
I like to clear decimals by multiplying by 10
141
94
= 3/2

What did you notice?

8. Again look at Page 230 for the figure
We are finding the following Ratios:
PQ:TU 2.6:6.5 or 26:65 = 2:5
QR:UV 1.2:3 = 12:30 = 2:5

Perimeter of PQRS: Perimeter of TUVW
You need to add up all the sides of each of the figures
2.2 + 2.6 + 1.2 + 3 = 9
and 5.5 + 6.5 + 3 + 7.5 = 22.5
9:22.5 = 90:225 = 2:5

What did you notice here?


For exercised 9-12 you need to use the Table on Page 230 as well

9. The population of Centerville in 1980 to its population in 1970?
44/36 = 11/9

10. The growth in the population of Easton to its 1980 population.
You need to subtract the 1970 population from the 1980 population to get the growth so
28-16 = 12 12/18 = 3/7

11. The total population of both towns in 1970 to their total population in 1980
36 + 16 = 52 and 44 + 28 = 72 52/72 = 13/ 18

12. The total growth in the population of both towns to their total 1980 population
Like number 10 you need to subtract to find the growth
(44-36) + (28-16) = 8 + 12 = 20
44 + 28 = 72 (from before)
20/72 = 5/18

13. During a season a baseball player hit safely in 135times at bat; the player struck out or was fielded out in 340 times at bat. What is the player’s ratio of hits to times at bat?

You take the 135 + 340 = 475 (the total times at bat)
135/475 = 37/95

14. A fruit drink recipe requires fruit juice and milk in the ration 3:5. What fraction of the drink is milk? What fraction is juice? Remember we need to find the total first. 3 + 5 = 8
so the fraction that is milk is 5/8 and the fraction that is fruit juice is 3/8

Math 6H ( Periods 3, 6, & 7)

Ratios 7-6

In our textbook, the example given involves the number of students --at what I called a mythical middle school --as well as the number of teachers. There are 35 teachers and 525 students. We can compare the number of teachers to the number of students by writing a quotient


number of teachers
number of students

35
525

1/15

The quotient of one number divided by a second number is called the ratio of the first number to the second number.

We can write a ratio in the following ways:

1/15 OR 1:15 OR 1 to 15

All of these expressions are read one to fifteen.

If the colon notation is used the first number is divided by the second. A ratio is said to be lowest terms if the two numbers are “relatively prime.”
You do not change an improper fraction to a mixed number if the improper fraction represents a ratio


There are 9 players on a baseball team. Four of these are infielders and 3 are outfielders. Find each ratio in lowest terms.

a. infielders to outfielders

b. outfields to total players

# of infielders
# of outfielders
= 4/3 or 4:3 or 4 to 3



# of outfielders
# total of players
= 3/9 = 1/3 or 1:3 or 1 to 3

Some ratios compare measurements. In these cases we must be sure the measurements are expressed in the same units

It takes Zoe 4 minutes to mix some paint for her science project. It takes her 3 hours to complete painting her science project. What is the ratio of the time it takes Zoe to mix the paint to the time it takes Zoe to paint her project?
Use minutes as a common unit for measuring time. You must convert the hours to minutes first

3h = 3 • 60min = 180 min

The ratio is :
min. to mix
min. to paint

= 4/180 = 1/45 or 1:45

Some ratios are in the form

40 miles per hour or 5 pencils for a dollar
“ I want my… I want my…. I want my … MPG!!”

These ratios involve quantities of different kinds and are called rates. Rates may be expressed as decimals or mixed numbers. Rates should be simplified to a per unit form. When a rate is expressed in a per unit form, such a rate is often called a unit rate.

Aubrey’s dad’s car went 258 miles on 12 gallons of gas. Express the rate of fuel consumption in miles per gallon.

The rate of fuel consumption is

258 miles
12 gallons

= 21 1/2 miles per gallon

Some of the most common units in which rates are given are the following:
mi/gal or mpg miles per gallon
mi/h or mph miles per hour
km/L kilometers per liter
km/h kilometers per hour