Download motion word problems

Word Problems Dealing with Unknown Numbers
First thing: ALL WORD PROBLES ARE DIFFERENT AND WORDED DIFFERENTLY. You can’t just do these
on autopilot. You really need to think and pay attention to what you’re being asked.
There are no concrete rules as to how to tackle a word problem but there are a bunch of things that
can help to tell you what to do.
Below is a list of keywords and what they usually mean.
KEYWORDS:
A number
How much
What
How many
How old
}
These words usually are what X or our UNKNOWN will be.
Here are some other common words. I’ve matched them up with their “math” meanings:
+
−
× or ∙
÷
=
<
≤
>
≥
( )²
( )³
Sum, add, total, plus, increase, more
Minus, difference, fewer, less, reduced, decrease, diminished
Product, times, of, at
Quotient, divided by, ratio, divided into
Is, are, was, equals
Is less than, at most
Is less than or equal to
Is greater than, at least
Is greater than or equal to
Squared
Cubed
1, 2, 3, 4… Consecutive (in a row) Integers
Let x, x+1, x+2… 1st, 2nd, and 3rd, consecutive integers (respectively) in “math” language.
1, 3, 5, 7… Consecutive ODD Integers.
Let x, x+2, x+4, x+6… Consecutive ODD Integers in “math” language.
THESE ARE THE SAME
2, 4, 6, 8… Consecutive EVEN Integers
Let x, x+2, x+4, x+6… Consecutive EVEN Integers in “math” language.
Step 1: Read through the WHOLE problem first. Don’t write anything down until you’ve read through
it at least once.
Step 2: What are you looking for?
Find what the unknown thing is and give it a letter (like x).
(HINT: SEE 1ST LIST OF WORDS)
Let x = whatever is unknown
Step 3: Look for key words to help with the math language.
Step 4: Set up the MATH language (translate the math DIRECTLY above/below the words in the
problem).
Step 5: Write the Equation!
Step 6: Solve it!
Step 7: CHECK IT!
Does the answer make sense?
Step 8: Answer then sentence. Make sure you answered all the parts. (Do you have all the numbers
they want you to find? All the lengths of the sides? All the ages of the people? Etc…)
SOME EXAMPLES:
Five more than three times a number is 17.
READ!
What are we looking for?
A number
So…
Let x = a number
Look for keywords:
Five more than three times a number is 17.
↓
↓
↓ ↓
↓
↓↓
5
+
3
∙
x
= 17
5 + 3x = 17
NOW, SOLVE IT! DOES IT MAKE SENSE?
MOTION WORD PROBLEMS
When dealing with motion problems you will see the words miles per hour or MPH
The EASIEST way to sort out your information given in the problem will be to MAKE A TABLE that
looks like the one below:
The moving object can be anything, a car, a train, a plane, a trip, anything.
Rate
(mph)
Time
(Hour or Hr)
Distance
(Miles or mi)
Moving object 1
Moving object 2
EXAMPLE:
1.) A passenger train and a freight train start at the same time from stations that are 405 miles apart
and travel toward each other. The rate of the passenger train is twice the rate of the freight train.
In 3 hours, the trains pass each other. Find the rate of each train.
We need to translate the above and then fill in the table with that information. From here we can make
an equation to solve the problem.
ASK YOURSELF THE FOLLOWING FOR EACH PROBLEM AND THEN FILL IN THE TABLE:
1.)
2.)
3.)
4.)
What are the moving objects?
Which of the objects’ rate will be x?
What will the other object’s rate be compared to the first one (x)?
What is the time traveled for each object?
Rate
(mph)
Time
(Hour or Hr)
Distance
(Miles or mi)
Freight train
x
3
3x
Passenger train
(2x)
3
3(2x)
5.) What was the total? The total distance traveled was 405 miles.
COIN WORD PROBLEMS
(Number of coins/bill/stamps) • ( Value of ONE coin/bill/stamp) = Total Value of coins/bills/stamps
The EASIEST way to sort out your information given in the problem will be to MAKE A TABLE that
looks like the one below:
Number of Coins
Value of ONE Coin
Total Value
Coin Type 1
Coin Type 2
NOTICE: THERE MAY BE MORE THAN 2 TYPES OF COINS USED
EXAMPLE:
1.) Bill has 4 times as many quarters are dimes. He has $2.20 in all. How many coins of each type
does he have?
Number of Coins
Value of ONE Coin
Total Value
Quarter
4x
25
100x
Dimes
x
10
10x
220
100x + 10x = 220
110x = 220
110
110
x = 2 Dimes
4x = 8 Quarters
MORE EXAMPLES:
1.) The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
2.) One number is twice another number. When the larger is diminished by 10, the result is 5 greater than the
smaller. Find the numbers.
3.) The sum of two numbers is 95. The larger number increased by 21 equals the smaller numbers increased by
32. Find the numbers.
4.) Seven times the larger of two consecutive integers is 43 less than 8 times the smaller. What are the
integers?
5.) The sum of three consecutive even integers is 1236. What are the integers?
6.) Six times a number minus eleven is 43. What is the number?
7.) The difference between one-fifth of a positive number and one-tenth of that number is 10. Find the
number.
8.) If two-thirds of a number is decreased by 30, the result is 10. Find the number.
9.) If the sum of two consecutive odd integers is divided by 4, the quotient is 9. Find the numbers.
10.) The larger of two numbers is 12 less than 4 times the smaller. If the smaller number is equal to one-third of
the larger number, find the numbers.
11.) There are two consecutive integers. If seven times the larger minus three times the smaller is 95, find the
integers.
12.) Two trains started at the same time from station which were 360 miles apart and traveled toward each other.
The rate of the fast train exceeded the rate of the slow train by 10 miles per hour. At the end of 2 hours, the
trains were still 120 miles apart. Find the rate of each train.
13.) How far can a man drive out into the country at the average rate of 60 miles per hour and return over the
same road at the average rate of 45 miles per hour if he travels a total of 7 hours?
14.) Two cars start from the same point at the same time and travel in opposite directions. The slow car travels at
56 miles per hour and the fast car travels at 60 miles per hour. In how many hours will the cars be 464 miles
apart?
15.) Kelly received a play purse from her Grandfather that contained 25 coins worth $2.00. If the purse contains
only nickels and dimes, how many of each coin are in the purse?
16.) Josephine has $7.70 consisting of dimes and quarters. The number of quarters is two more than twice the
number of dimes. How many of each kind does she have?
17.) Manuel has 3 times as many quarters as dimes totaling $6.80. How many of each coin does he have?
18.) Jerry, the postal clerk, sold 80 stamps for $19.10. Some were 20 cent stamps and some were 30 cent air
grams. How many of each kind did he sell?